The vinegar dosing is for nutrient control and ultimately that is always the only real answer. Peroxide can help to break the cycle of algae growth but it will just keep retuning until nutrients are under control. As
@Nick James said then you won't be able to grow algae if you try....
My system has every type of algae around in it but it's a little tuft of one here...a couple of bubbles up under the rim at the water line a bit of film in a back corner...that you can find it you look for them. They all add to the biodiversity and compete with each other for the small amounts of nutrients available. If/when I have the time to maintain the tank at the level for SPS, even these traces will disappear.
Hair algae (not Bryopsis) is really very delicate all things considered, more like grass rather than weeds since it has such high nutrient demands... As you truly get a handle on your nutrient situation, it will be the first specie to diminish to traces.
Additionally, once you have a solid growing culture of coraline algae and/or huge growing colonies of SPS they will be giving off such a volume of algicidal compounds that even if nutrients rise, the algae will not be able to grow. That is the actual secret behind the thriving high nutrient established reefs you may read about online.