ChemiClean works really well to clean up your cyano in about a week. After you get rid of it, it may come back as red slime algae which means you are having a problem with phosphates and you will need to get rid of your phosphate problem. One of the more common sources of phosphates is using a cheap brand of GAC. Black Diamond is a good brand as is Seachem to use as your GAC. They have extremely low phosphate leaks. To eliminate your current phosphates there are various products you can get, some being filter pads, others being filter media.
Water changes will definitely help but it's like if you had a pool with a sewer pipe leaking sewage into your pool. You can do water changes to help decrease the sewage but what you really need to do is shut off the sewer pipe. Same thing with treatments. You can dump chemicals in to get rid of it but it's going to keep coming back until you find the source. Even though it is technically not an algae, you cure it in similar ways. Reduce excess food, reduce lighting, and in the case of cyano get rid of the phosphates in your tank.
The water flow from powerheads helps keep the cyano from being visible, but only by keeping it from settling. It doesn't actually remove it from your tank.