Most of us have a natural tendency to "do something" when we perceive a problem. Often this is very unwise. Jumping into "cures" when the tank is obviously still in a state of flux, i.e., not yet settled biologically, usually makes it worse.
Phosphorus is a vital plant nutrient, but one that is required in low amounts and there is always sufficient in the aquarium. It arrives in fish foods as phosphates. And in this present case, apparently in the source water (tap water) too. Diana Walstad writes that in her aquaria, phosphate levels are between 1 and 5 mg/liter, more than sufficient for algae. Even an aquarium with phosphate at 0.15 mg/l will have more than enough for algae.
Although algae is always more adept than plants at using light and nutrients, it is a fact that ponds, aquaria and lakes with dense plant growth often have little algae. And this brings me back to the balance. Increase the plants, limit the light, and allow the aquarium to stabilize biologically. If Diana can have algae-free aquaria with phosphates as high as 5 mg/l, you should be able to have the same with 1 mg/l.
How long is the light on daily? And how often do you dose with Flourish, and presumably it is the maximum recommended on the label? And what plant species have you?