Loganair/BA franchise agreement
Loganair have more to gain from withdrawing from the franchise agreement than BA have from getting rid of them.
BA have made millions from Loganair and I would think it is no longer in LC's interest to remain a BA franchise partner. I can't see however, how it would benefit them by going it alone. To become a franchise partner for another airline would be a better option, it would save the cost of setting up their own ticketing and reservations department and the only costs involved would be the repainting of their aircraft and some new uniforms. The lead airline would get paid a pile of cash (although perhaps not as much as BA got) for doing very little.
I can't see a Flybe takeover being on the cards given the problems they are having, a franchise agreement with Loganair would make more sense.