Bin BBMF?
My apologies for any egg sucking. The flight is named for the RAFs most famous air battle and was originally only equipped with fighters that represent some of the types that fought in the Battle (Hurricane, Spitfire, we can quibble on Marks). The bomber was a later addition and represents the huge losses (55,573, a 44.4% death rate) faced by bomber command aircrew.
The Dakota replaced the Dove/Devon for multi engined training and then she became a display item in her own right and not only represents the RAFs cargo, troop and aeromed operation, but is also a visible symbol of the UKs airborne forces.
Chipmunks? Tail dragger training tools. Yes, the name could change to more acurately reflect the current aircraft mix, just 'memorial flight' might be better, but BBMF is fine imho. The inclusion of civilian 'warbirds' has been done, and BBMF aircraft have flown many times in mixed formations (Duxford, RIAT, Waddington), however the recent inclusion of a Typhoon and Spitfire/F-35 and Lancaster display not only 'steps things up' but also display the vast change in the RAFs combat airpower.
Behaviour was mentioned, I don't know about RAFAT, but for BBMF I would put this down to the veterans who visit the flight (or the flight visting them) both at home and at various events in the UK and abroad. A few minutes in their presence is more than enough to check the ego at the door and to remain level headed/sensible.
All gave some, some gave all. Lest we forget.