Under normal circumstances I would just assume that he got a BFR elsewhere unless you know for fact that he didn't, since a CFI does not have a moral responsibility to be a detective or FAA enforcer.
However, if you have REASON to suspect that he did not (or was incable of) getting a BFR from someone else you might talk to the FSDO.
I'd be very reluctant to do this, but the young eagles thing might tip the scales on that.
You have to go with your gut...if you suspect he's not legal to fly kids around, better speak up. In fairness to the guy, don't give the FAA a lot of ammo about the guy's bad attitude and poor skills...coming from a CFI, that alone could get him a 709 ride even if he is legal. Just express concern that he might not have completed a BFR.
If he is legal, involving the FSDO should not harm him...they should just look at his logbook and medical.