Flybe (as an operator), have no responsibility for operational or commercial performance for the Flybe branded, Stobart Air operated services at SEN. The responsibility for EU261 lies with the operator of the flight, not the company under which the flight is branded.
When you purchase a flight operated as a codeshare, you may have booked through one airline but be travelling with another. It can't be the responsibility of the airline that you purchased the flight from to pay compensation if they have no influence or part to play in delivery of the service by the partner airline. That said, you'd hope that there would be strong internal comms between the two companies that would result in the customer not having to do the leg work. This would surely be a better solution.