I personally scrub the dock I have for my turtles once a week. Sure it's a little green but I figured they put it there and it doesn't bother them lol. The one time it really bugged me. I tried to sterilize it in bleach and water. I left it in the mix for 2-3 days then I completely rinsed and scrubbed it and allowed it to fully dry before putting it back in the tank.
If I were you, I would try exploring what is causing the algae and trying taking care of it from there :)
It's very essential that you have the proper lighting and filtration for your turtle. Telling me how long you have it doesn't really help :( I need to know it's shell length. It sounds young to me.. so if it is a submersible water heater is also highly recommended.
I don't have anything that comes to mind in which you can use to cover your flagstone... I'm going to assume that is a dock. I wouldn't even recommend covering it with plastic because turtles have the ability to bite through things. It is in their nature to be gathers, explore, and hunt for their food so it is very likely your turtle will bite through and attempt to eat plastic... I don't know how much paint would help but I know there are some non-toxic paints out there. You would have to do your research. As for spray paint, I don't think there is any safe type.
Figured I would ask you a ? directly....I have a hatchling, approx. 3 months old in a tank that I placed flagstone in for him to climb, bask, etc. I currently am unable to buy a filter for him so I have been cleaning his tank and scrubbing the algae off the flagstone every 3-4 days or so. I was thinking of using something to 'seal' the flagstone so I can just rinse them with soap and water instead of the algae growing in the nooks and crannies where I am unable to fully scrub. Clear spray paint or something similar, I'm wondering if this is unsafe. Don't want to jeopardize the little guy.