It's a near-certainty that the flue itself is sound. If it is cracked, you would see some smoke damage.
I don't think replastering solves the problem, and your experience seems to be forcing the same conclusion on you. I suspect that some mortar joints in the wall have given way, and perhaps a block might have cracked -- all because of heat expansion. If the crack is not wide, but more of a cosmetic problem, then it might be better to hide it rather than try to fill it. I have used a mirror from mantel-shelf to ceiling to do that.