In the meantime there are just 8 788s and they are used heavily. Unless BA can identify a route that is operated by 788s which is ready to move to a larger plane without destroying its economics, or is so bad it should be terminated, there simply aren't any 788s available for the next two years to launch or reactivate routes.
There's another option too:
they could always have AA op/turn a 787 via LHR and operate an extant route/frequency on their behalf.
Yes, they certainly could, but obviously only on a route to/from the USA, as AA don't have rights to operate from the UK to anywhere else.
At the moment that is just the BA188/189 rotation on EWR-LHR-EWR, as all other BA 788 routes go outside the USA. Shortly this rotation is moving to BA 789 aircraft, so no 788 would then be released if AA operated it.
As part of the reshuffle as the last of the long haul 763s leave the main BA fleet over the next 8 weeks, the BWI flight will instead become a BA 788. However there's some doubt as to whether this could be operated by AA without invalidating the revenue guarantee agreement between the State of Maryland and BA.
So we're left with an AA 788 operating any new/restarted route between the USA and the UK. Really, why wouldn't they just fly that as AA rather than BA? Under the JV, it makes no difference at all in revenue terms and might save money in administration costs - AA almost certainly already have ground handling in place at any US airport that might be worth considering.
Now of course if there is a route BA could open/reopen that would support a 789/772/77W from day 1 then using an AA plane on a current BA rotation for a similar aircraft would work, as long as care is taken to choose a route that has no BA First now, or has alternative flights that do have First, or AA can spare a 77W for.