I'd be surprised if BA management even noticed - they don't give a stuff about flying in the UK regions now and have regularly had non-BA liveried aircraft operating subcharters over the years both by franchisees and on their own mainline domestic services too. Given that BA own 15% of flybe and codeshare with flybe on certain routes I hope they might allow a small operator like Loganair to operate the odd flybe liveried aircraft where operational requirements demand it. Agree the 340 looks good in flybe colours - hope the new franchise works well for them.
There is also a huge difference to BA between easyJet branding and FlyBe branding (flybe is also a company in which they have a commercial interest).
From a BA perspective, easyJet is not only route competition - it is also the low cost underclass of airline from which they differentiate their offering psychologically.
Quite apart from the direct effect on passengers and marketing to them - can you imaging the
PR damage that would come from stories in the media about BA using 'easyJet aircraft'.
With Logan/Be this is less of an issue due to pax familiarity - and it is effectively a non-issue due to the commercial interest and recent history (the fate of BA Connect)