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Generally this is the most expensive way to fly either BA or FlyBe, per mile. I sometimes use the codeshare arrangements (e.g. starting at those Scottish airports which don't have APD) but generally it's a poor deal.
However, yes you will get Tier and Avios points.
And you will get the restricted FlyBe hand luggage. Their planes are not generously sized and at certain stations (MAN comes to mind) they can be tough on hand luggage too, though not consistentlly so.
For checked luggage you are supposed to get the BA allowance, but I can well imagine a FlyBe check in agent not being aware of this. So I'd keep it down to one bag if possible.