I'm not sure about Flybe. Their experience at BRS in the past has not always been positive, not least because easyJet came onto their French routes in the past leading Flybe to abandon them. easyJet seems set on further growth at BRS and Flybe might be concerned that lightning would strike again.
Anyway, they have bases at EXT and CWL although I don't know how successful they are in attracting passengers from the BRS core catchment.
Some of the airlines that B_T suggests would be in competition with easyJet to such cities as Vienna, Copenhagen and Madrid. I'm not sure that there would be sufficient demand for competition on these routes - maybe Madrid.
If the 'strong rumours' have legs then all sorts of airlines are possible, some obviously less likely than others: Jet2, Vueling, Norwegian, Eurowings are a few of perhaps the more unlikely ones but, outside these airlines and the airport, who knows?
Turkish Airlines were rumoured strongly to be looking at BRS a couple of years ago with one or two serious aviation analysts suggesting that the airport was on the airline's radar. That seems to have gone quiet. Qatar is also being talked about again in the BRS 'chattering classes' but that may be wishful speculation at the turn of the year coupled with a report a year or so ago that the Qatar UK chief said that they were looking at the South West.
As we keep saying, for an airport with such physical limitations, poor surface connectivity and unhelpful weather at times (although perversely BRS has seen a large number of inbound weather diversions this week from other temporarily closed UK airports) its continual passenger and route expansion shows the potential market that exists.