Maybe it's user error, but where do you see the gate info on the BA app (on Android, in case they're different)?

My unscientific (due to low sample size) test was to go to Flight Info -> search by flight -> enter 564 [which departs in 30 minutes] and get no gate information at all.

I then did Flight Info -> search by airport -> LHR and got a list of flights departing very shortly, none of which had gate information.

And then, of course, no gate info on www.ba.com/arrdep, which would make lots of sense if it was there as well (any smartphone and computer have a browser).