Also depends which BA flight you are on, you can check bags for the later one whilst the earlier flight check is staffed. However, the museum is only open until 1730 so that potentially gives you just over an hour by the time you have got there.

Agree on the other advice that it may be easiest to leave bags in the car (if you have one).

I went [again] a few weeks ago and it was excellent. Easily enough for an hour and a half to 2 hours+. It's also got the Bell X-1 in it which seems to have moved from the Smithsonian on the Mall.