High nutrients are one of the major part of causing cyano algae. If you blow it , they will bloom somewhere else. Keep up with your water changes and cut down on feeding and siphon all the debris / cyano off the tank.
If they get worse...use chem-clean but this will not cure the main problem and it's a chemical. Mostly all reef tanks get cyano once in a while due to high nutrients or immaturity of the tank.
Yep , I have it also and it's fading away now that I'm doing my water change once a week and reducing my feeding frenzy.
BTW, cool clown!