Just in case others might get confused with the addition of BIA which I personally thought was a strange omission but just to clarify on kcockaynes excellent recollections it was
Jersey Airlines, BU(CI)A, BIA, Air UK and finally KLM UK until it was finally absorbed into the KLM City Hopper operation.
As kcockayne clearly states there is no connection with the above and the history of Flybe.