But that's a lot of effort for a sparrow. What I did last time was open the flue and close the glass front on the fireplace. Over time the bird DID find it's way in there and I open the glass front just enough to get access and covered the bird with an old sheet wrapped it up as gently as possible and let it go outside good as new.
If you've opened the flue and the bird doesn't come out on it's own, there's not much YOU can do short of calling someone else, IMO.
Depending on the type of bird they won't have a very long life span if they're flying around in the chimney because their metabolism is so high.
But you definitely need to have your chimney capped properly so that birds can't get in. If you've had two in there in a short span you can almost be assured you'll get more and they may even be trying to nest in there.