im a big believer in patience. you have excessive cyano because your tank does not enough have "good" bacteria/algae in your tank which outcompetes the cyano. just give it some time. might take a couple months or even more.
stuff like chemiclean is essentially an antibiotic. it will help, as cyano is basically a bacteria, but it does affect other bacteria in your tank too. but if you want a quick fix yea it should help, just be mentally prepared that it will come and go lo.
if you want to go the "natural" route (patience), just elevate your KH slightly (Julian Sprung recommends above 8) to help. increasing flow around cyano growth area helps too.