Flybe, like all budget airlines, operates a 'point-to-point' service only and doesn't recognise connecting flights.
Even if you were to fly from Belfast City Airport to Glasgow with Flybe, and then from there to Jersey with exactly the same airline, you'd still have to collect your bags from the first flight, go through the departures area and then around to the check-in area. Further, if you missed the second flight because of the late arrival of the first one, they'd almost certainly say "Nothing to do with us mate. We don't recognise the concept of 'connections'. You'll have to pay again for another flight to Jersey".
It's exactly the same with Ryanair, easyJet and all other budget operators. Each sector of your journey is regarded as entirely separate (irrespective of whether successive sectors are with the same airline or with different ones).
Budget airlines typically allow just 25 minutes to get all of the passengers and luggage off an incoming flight, clean the aircraft, refuel it, carry out all the pre-flight checks and then load all of the passengers and their luggage on for the next flight. (It's by ensuring that their aircraft are nearly always in the air that they can keep their fares so low). Their ground handling agents simply don't have time to deal with the complications that can arise when bags are transferred directly from one flight to another.