Don't see how relocating elsewhere would make sense. Flybe currently serves INV, NCL, GCI, JER, BHD, IOM and NQY.
INV: easyJet will simply ramp up capacity from LGW and LTN.
JER: I suppose BA will add some capacity at LGW or start up from LCY and easyJet (or another airline) is likely to open a route to JER from LGW. Probably some opportunity for BE to extend seasonal flying from LTN, but the main customer base will be catered for from airlines that remain in business at LGW. At STN, traditionally a rather poor C.I. market with a lot of airlines coming and going, they would have to push out Blue Islands.
NCL: My gut feeling is that this is a route BE cannot transfer to STN, SEN or LTN as it caters for a specific "south of London" catchment area. It is a marginal anyway.
BHD: I don't see the point of serving BHD from LTN, STN or SEN in competition to existing BFS services at those airports by easyJet. Who would make the trek to SEN or STN instead of flying to BHD from LHR or simply switching to LGW-BFS?
NQY: If easyJet is not interested in serving LGW-NQY, I could see it work for BE from LTN as the Cornish market will simply will have to accept whatever is offered as the LON terminus. But as easyJet alreadly serves NQY from SEN, I doubt that they would be uninterested in flying from LGW by moving and expanding its SEN-NQY operation.
IOM: Here I can see LTN as an option as IOM-LTN has a bit of a tradition as a farecracker route. But it really depends on how much additional capacity easyJet would deploy on LGW-IOM. If they only add a second daily flight, it owuld leave some space for Flybe to do a double daily into LTN.
GCI: I suppose Aurigny will add capacity to LGW and STN and that's it. Maybe Blue Islands throws in LCY for the fat cat business if decent slots are available at LCY.
In short, most of Flybe's LGW business will be taken up by other airlines, so there is little point of replicating the existing LGW network at one of the north/east London airports.