KLM and Flybe code sharing comes up occasionally and as I understand it, KLM have an agreement that with one or more of their unions that they will code share on no more than two routes to each country (presumably to protect jobs at KLM).
Currently KLM and Flybe code share on SOU-AMS and INV-AMS so unless something changes, I'd be surprised to see them code share with Flybe to MAN.
Flybe operate to AMS from BHX and do not cooperate with KLM.
Pity really that the arrangement which works well with Air France cannot be extended to KLM.