Edit: This seems exactly what Blue Islands are doing today.
Indeed, BI are offering to fly people with a Flybe reservation for free today, or if no reservation for a £50 all-in walk-up fare at the airport.
This is until they have their own booking engine up and running, which they say they hope to do by Monday, if not sooner.
They are also operating replacement flights from the islands to EXT and BHX today - not normal routes for them.
Good for them.
Also don't understand why the Stobart-operated former Flybe franchise flights could not carry on in a similar way?