Check your Phosphate levels first, then your nitrates.
Red slime or cynobacteria is a bacteria. Therefore you could use a antibiotic to assist you in controling it, however you also will help to kill the benificial bacteria that you need. You can use red slime remover. another chemical. You can use chemi clean......but first heres what I would do.
Check your phosphate and nitrates to help you find out whats going on. At the same time have your top off water checked for those two as well. If you feed frozen food, stop, for a while. Many frozen foods contain phosphate. Depending on how bad your cyno is you might need to syphon some of it out thereby doing a whater change but check that top off water first. If your using tap water change to RO water.
Thats where I'd start.
Thomas