Good 'ol terminology confustion one.
There is only one Battle of Britain Memorial Flight the 'owners' of the BBMF acronym - and indeed based at Conningsby, and coming to airshows across the UK with the Spitfires, Hurricanes and Lancaster.
There are any number of Battle of Britain memorials, museums, monuments etc - most of which are very good, and most of which are in S.E. England for very obvious reasons!
Cheers
JamesK