why the assumption that it would be a US flagged base?
no one would, i assume, think that either the RAF or USAF has the money or inclination to reactivate a mothballed base and build significant infrastructure there for just a handful of aircraft to operate from - when the RAF RC-135 fleet is at full chat there'll still often only be one in the UK, how many USAF RC-135's are usually sat on the ramp at Mildenhall?
if such a thing happens i'd put good money on the US put its visiting RC's at Waddington..
Waddington isn't the TARDIS that many seem to think it is - how many more types can you fit in there? And remember it's not just the actual jets you'd need to consider; Eng, Logs, accommodation etc all need to be factored in.
And don't just think USAF RC-135s. When you consider they also operate 135 variants such as the OC-135 and the E4 out of Mildenhall, not to mention AAR then it starts to make sense to consider a centralised 135 facility for all types.