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...