Yup, sounds like cyano.
Regardless of your flow, you need to get to the source of the cyano algae's food source - no food = dead algae.
It does appear to be phosphates as your nitrates are apparently 0.
Let's try to narrow down the source of phosphates.
1. Water: whatever the source of the water you're putting in your tank is, test it for both phosphates and nitrates. If you get any at all, then your only solution is to go RO/DI water.
2. Media: phosphates (and nitrates) love to build up in filter media. Get rid of it as soon as possible if you're using floss or sponges. But before you toss it, test it to see if this is the source. Secondly, certain filter flosses are phosphate repositories! Put a bit of CLEAN floss into a cup with a bit of water and test for phosphate.
3. Substrate/live rock: over time detritus can can collect and rot on both the live rock and substrate, especially if you have the wrong combination of clean-up creatures to process it. If you don't regularly siphon it out or have a deep enough sandbed for nitrification, then this is your phosphate source. This is the trickiest because as the phosphate resides in the substrate/rock (where the cyano feeds off of it), there's none to test for in the water column. As a result, your tank could be full of phosphate yet your test kit would read zero!
4. Something dead: Missing any residents? Depending on your tank's size, a dead fish or three can quickly pollute the tank.
Other solutions:
Low flow is not a cause of cyano per se, but can result in cyano because the detritus in the substrate/rock is not being blown around enough to be dealt with by the filters/skimmer. Increasing flow prevent the build-up of detritus.
Get some macro-algae to compete for the phosphates. Caulerpa in its various forms is cheap and popular (except in California), but has a nasty habit of "going sexual" and polluting the tank. Chaetomorpha is a good alternative.
The only commonly available creatures that will feed on cyano are certain nudibranchs (sea slug) the most popular being the lettuce nudibranch (elysia diomedea). They can be tricky to keep alive, however, if there isn't any cyano left around for it to eat. That's why I know of at least one nudibranch that's been passed around locally amongst hobbyists like some kind of hot potatoe.
As a last resort, you can go the chemical route. The most well-known among them is Boyd's Chemi-clean. If you do chose this route, your absolutely MUST follow the directions to the letter or you WILL end up with a dead tank. These are powerful chemicals, some containing antibiotics that can kill indiscriminately. Also understand, that while the chemicals can get rid of the cyano, will may only be temporary as you have not addressed the source of your phosphate problems.
