Couler has several meanings, one is similar to “to flow/to run” (l’eau coule), another common is “to sink” (le bateau coule.)

Fluer means “to flow”. This verb is almost never used nowadays, however, there a many usual French words sharing the same Latin roots:

• refluer (reverse flow)
• confluent (joint flow, confluence)
• affluer / affluent / affluence (flow to the same location)
• influer / influent / influence (affect the flow)
• effluve (emanatig flow)
• fluide (that flow)
• fleuve, fluvial (a flowing river)
• fluor (originally, a liquid chemical substance)
• flot (flow)
• flotte (fleet)
• flotter (to float)
• superflu (originally, that overflow)

It is interesting to observe the English “fluent” which was obviously originally a French word is now considered an foreign word. Sometimes people say for fun “Il est fluent en anglais” but this is clearly considered an anglicism.

Recouler is rarely used and when it is, it might either mean “sink again” or “flow again.”

Refluer means to flow in the opposite direction, like in a reflux (a backflow.)

Fluer vs Couler

Both verbs have the same meaning nowadays when talking about a flow of liquid but are absolutely not used in the same way.

Fluer (from Latin fluere "couler, s’écouler" → to flow).
The verb has kept the meaning it had in Latin but nowadays in French it is considered archaic and very literary and is only used as a technical word, chiefly in medicine when talking about the flow of organic fluids.

Couler (from Latin colare "filtrer, épurer" → to filter, to purify). It is the usual verb used when talking about the flow of all sorts of liquids, be it from the tap or a bottle, the course of a river, molten metal, etc.
It is used figuratively also, when talking about time.
It is used as a transitive verb to mean that you cast a piece of metal (letting the molten metal flow).

Chaque moule fabriqué est destiné à couler une pièce unique.

Refluer vs Recouler

Both verbs are derivative verbs formed with different meanings of the prefix re- and have different meanings.

Refluer comes directly from the Latin refluere where the prefix re- indicates a backward motion. It means to flow in the reverse direction.
It is commonly used in French when talking about the retiring tide, the course of a river or of a drain that will flow in the reverse direction.
It is used figuratively when talking about a mass of something that will move backwards. For example :

Les CRS [ont] chargé les manifestants qui ont ensuite reflué vers la place de la République.

La perte de la bataille de Waterloo fit refluer un grand nombre de prisonniers français dans les villes des Pays-Bas (Chateaubriand)

Recouler is formed from the French verb couler and prefix re- meaning “again”.
It could be used to indicate that water is once again flowing where it had stopped flowing.

La source a longtemps été à sec mais l’eau recoule désormais.

This use is possible but I expect most French people would use "coule à nouveau" in that case.

It is used mostly to express that one will cast again a piece of metal.

When re- means again, it’s sometimes hard to know if it’s a real word (recouler, remanger, refaire exist with re- meaning again), or just a way of speaking putting re- with any verb or word, in order to mean again:

Rebonjour = Bonjour encore une fois = Hello again

Je revais au cinéma ce soir = Je retourne* au cinéma ce soir = I go back to the cinema tonight

J’ai recassé ce vase = J’ai encore cassé ce vase = I broke this vase again

*speaking about re- meaning again… it’s not the case here, retourner doesn’t mean tourner encore (well, it could in some context) but to return/to go back, in this context.

The use of re- in WTF new ways is a part of spoken French, sometimes just for fun and sometimes like if it was correct.

And you can even (still in spoken language) put many re- if you want to show the number of times: cet été je suis rereretourné en Angleterre, meaning it was the forth time (retourner = to go again, + 2 times re).