Some people insist the water be so clean not only COULD they drink it, but they WOULD. Personally, that's a bit overboard for me. As long as the water was clean when it went in the waterer and the waterer is reasonably clean, I'm okay with it. They're not humans, they're chickens and I am not going to spend all day policing the cleanliness of their waterers. If they want to dirty it up, so be it, they're the ones that have to drink it.
That said, I wouldn't use the water from your rain barrels unless you use the water up relatively quickly -- but from the sounds of the algae, that's not the case? -- simply because water that sits can get stagnant. I'm not sure there's any direct threat to the birds, but it's just not something I would do.