Not sure where Flybe's slots for NQY come from (GCI is operated with ex Cobalt Air slots). Just tried to find something out about it and found an article from the Independent that they were part of the IAG/BD merger remedy slots portfolio. Straightforward use of such slots is unlikely though, as those slots are route specific and NQY and GCI are none of the handful of routes that are covered. However, the FT mentioned in an article that the government allowed Flybe to "repurpose" its existing slots at Heathrow, which suggests that the slots are indeed former remedy slots (but probably not those for ABZ and LHR as those routes continue to be operated by BE). Before, my suspicion was that BE was babysitting/grandfathering slots for VS, but this does not appear to be the case. If they are using remedy slots, the interesting question is what owuld happen if an airline shows up that intends to serve one of the orutes for which they were designated as remedy slots in 2012 (e.g. Cairo, Riyadh, Nice).
As for PSOs at LHR, I don't think there is currently a mechanism for automatic access to LHR if the route is operated under a PSO scheme. Making slots available for PSOs in the future has been used as a bait by the airport in the discussion about an expansion of LHR, though.