Like human relationships, different trainers get on better with different types of horses and plenty would be better off in a different stable.
Flemenstar, however, is doing very well where he is, he jumps well, is in good health, has no fitness issues and appears to enjoy life. He is also slowly learning to settle better.
He appears to be a straightforward horse and I would be surprised if another trainer could improve him as an athlete, which leaves the question about how to campaign him. It can't be easy dealing with an opinionated owner, even for a bigger trainer (as Henry de Bromhead might attest). Any bluff a small trainer might try such as saying he must be allowed to dictate or the horse will have to leave is likely to be called.