In Deleuze and Guattari’s collaborative works in the original French the word « flux » crops up constantly and is a central technical term in their philosophy. The English translations render this one French word randomly as « flux » or « flow », jumping from one translation to the other even within a single paragraph.
In English the word « flux » is a term appropriate to more technical, more quantitative (even vaguely so) discussions, « flow » is employed in less technical, or more qualitative contexts.
On the technical side, we may think of thermodynamics and its vocabulary of fluxes, and this is indeed relevant to Deleuze and Guattari’s network of multi-disciplinary references, but for « flux » I think the intended reference is at least as much to history, sociology, and economics as to physics.
In the preface to the Italian edition of A THOUSAND PLATEAUS Deleuze sketches out a three point summary of ANTI-OEDIPUS. Point 3 is about fluxes:
« Universal history indeed exists, but it is a history of contingency (the fluxes, which are the object of History, are canalized through primitive codes, the over-coding of the despot, and the decoding of capitalism which makes possible the conjunction of independent fluxes) ». Two Regimes of Madness page 309.
Note 1: the translation has « flows », I have replaced its two occurrences in this passage by « fluxes ».
Note 2: two commas present in the French text are missing in the English translation: after the first use of « fluxes » and then again after « History ». I have restored them so that the passage reads: « the fluxes, which are the object of History, are canalized » (instead of « the fluxes which are the object of History are canalized ». This radically changes the sense. With the commas we have a definition of « fluxes » as the object of history. Without the commas we have a limitation or selection of the fluxes.
Note 3: Deleuze’s prefaces to the English and Italian translations of his books are of extreme value, given that he explains himself so rarely.
Thus, for Deleuze and Guattari the « fluxes » are the « object of history », even if the meaning of this term is generalised to encompass an ontology of fluxes. The reference in the first instance is directed more to the work of Fernand Braudel and Gabriel Tarde than to that of Charles Fourier.
To sum up and push further my thoughts on the flux/flow conundrum: the term « flux » is both more quantitative (broadly defined) and more technical in connotation than « flow ». This quantitative/technical acception of « flux » is what is relevant to Deleuze’s use of the term. This conjecture is confirmed by Deleuze’s remarks on « fluxes » as the object of history and on the need to quantify fluxes, including writing.
On this idea of the quantification of fluxes, one may turn to the first paragraphs of RHIZOME where Deleuze and Guattari speak of the need to « quantify writing », taking it as one flux among many, and so the need to quantify the fluxes of any assemblage: speed, acceleration, viscosity, sedimentation, etc. Writing as more than literature
The quantifying criteria that Deleuze and Guattari enunciate at the beginning of RHIZOME concern all fluxes, including writing, and situate these fluxes within and between assemblages. Thus the habitual translation of « flux » as « flow » tends to nudge the apprehension and reception of ANTI-OEDIPUS in English more towards the literary pole than the original French text authorises.
A second problem is that the preference for the term « flow » makes us lose the intrinsic link between fluxes and assemblages (or better « arrangements » or « set-ups »). We move easily from « flow » to « free flow » and to a naive anarchistic interpretation of ANTI-OEDIPUS as « anything goes » or formlessness.
A further consideration, only implicit in ANTI-OEDIPUS but one that emerges very clearly in KAFKA (1975) and RHIZOME (1976) before receiving fuller expression in A THOUSAND PLATEAUS is that for assemblages there are no purely machinic fluxes, fluxes are also always also semiotic, and thus not only quantified but « indexed ».
« the flow and its quanta can be grasped only by virtue of indexes on the segmented line, but conversely, that line and those indexes exist only by virtue of the flow suffusing them » (A THOUSAND PLATEAUS, 218).
Terminological note on the quasi-synonymy between fluxes and lines:
Fluxes are both machinic and semiotic, they are situated between the ideal poles of pure sensations and pure representations, they are lines, becomings, percepts and affects. Deleuze and Guattari distinguish 3 lines: segmented, supple or molecular, and line of deterritorialisation (primary over the two others).
One must also distinguish the line traced (actualised) and the line that is tracing itself (virtual). Fluxes are quasi-synonymous with lines as they are being traced. F
We can say that fluxes and lines are « quasi-synonymous » because Deleuze and Guattari discuss them in the same terms and the same contexts, but that « flux » has a more active, material, hyletic, connotation and « line » a more orientational, conceptual, noetic connotation.
The fluxes both follow and trace the lines.
I am grateful for a discussion with Yan Grenier and Brooks Brown for pushing me to clarify my ideas on this subject.
AGENT SWARM 
might be of interest
https://www.listennotes.com/podcasts/acid-horizon/dialectics-of-the-gods-Q_XqIZr-F51/
« Grant Maxwell is the author of Integration and Difference: Constructing a Mythical Dialectic, A book which confronts the perennial problem of opposition in philosophy with respect to the notions of integration and difference. This is a robust work which covers many figures in Philosophy from Hegel to William James to Isabel Stegners. In this discussion we delve into the sections of the book that specifically concern the relationship between Deleuze and American archetypal psychologist James Hillman and the work of F.W.J. Schelling. »
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I haven’t read his book but sometime ago on his blog I found him to play a bit fast and loose with these figures and their histories and tried to offer a counter-reading but my replies years later remain « awaiting moderation », be interested in what you make of it all.
I’ve cut and pasted some of what I said that isn’t public on his blog:
his colleague David Miller taught a class comparing Hillman to Julia Kristeva’s Dark Sun period work but Hillman wasn’t moved by post-structuralisms which makes sense given his own tendencies along structuralist lines, he once wrote that rhetoric was the animal mode of human-being which brings to mind his brief mention of Wittgenstein (in Revisioning if memory serves) and that would have been a fruitful line of thought but he never could get over his own version of collective unconsciousness, Victor J Krebs (another Hillman fan) wrote a chapter on the Bodily Root of Wittgenstein’s work on perspicuous representations which fits in well with Jung’s feeling-toned complexes and I think with D&G as well as the later Richard Rorty who wrote: “In the Davidsonian account of metaphor, which I summarized in Chapter I, when a metaphor is created it does not express something which previously existed, although, of course, it is caused by something that previously existed. For Freud, this cause is not the recollection of another world but rather some particular obsession-generating cathexis of some particular person or object or word early in life. By seeing every human being as consciously or unconsciously acting out an idiosyncratic fantasy, we can see the distinctively human, as opposed to animal, portion of each human life as the use for symbolic purposes of every particular person, object, situation, event, and word encountered in later life. This process amounts to redescribing them, thereby saying of them all, “Thus I willed it.” Seen from this angle, the intellectual (the person who uses words or visual or musical forms for this purpose) is just a special case – just somebody who does with marks and noises what other people do with their spouses and children, their fellow workers, the tools of their trade, the cash accounts of their businesses, the possessions they accumulate in their homes, the music they listen to, the sports they play or watch, or the trees they pass on their way to work. Anything from the sound of a word through the color of a leaf to the feel of a piece of skin can, as Freud showed us, serve to dramatize and crystallize a human being’s sense of self-identity. For any such thing can play the role in an individual life which philosophers have thought could, or at least should, be played only by things which were universal, common to us all. It can symbolize the blind impress all our behavings bear. Any seemingly random constellation of such things can set the tone of a life. Any such constellation can set up an unconditional commandment to whose service a life may be devoted – a commandment no less unconditional because it may be intelligible to, at most, only one person. Another way of making this point is to say that the social process of literalizing a metaphor is duplicated in the fantasy life of an individual. We call something “fantasy” rather than “poetry” or “philosophy” when it revolves around metaphors which do not catch on with other people – that is, around ways of speaking or acting which the rest of us cannot find a use for. But Freud shows us how something which seems pointless or ridiculous or vile to society can become the crucial element in the individual’s sense of who she is, her own way of tracing home the blind impress all her behavings bear. “
https://syntheticzero.net/2014/06/02/james-hillman-culture-the-animal-soul-pdf/
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ps here’s a link to Victor’s paper that I mentioned
https://www.academia.edu/41178286/The_Bodily_Root_Seeing_Aspects_and_Inner_Experience
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here’s d.l. miller on rhetoric vs grammar in hillman
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