I doubt whether it is still flyable, it was reactivated for the now cancelled HSCT programme run by Boeing and NASA, to look at issues involved in maybe building a new SST.
Presumably it was used as BA
Concordes were busy serving their airlines, and none of the prototype, pre-production or or 1st two production aircraft were available, the UK one, 202, was little more of a hollow shell by the late 1990s after being used as a spares source by BA
since the mid 1980's.
-144 reactivated was re-engined with engines taken from a TU
-160 Blackjack bomber, maybe an attempt to provide it with some kind of decent performance for the research role, to be frank the TU
-144 was a lesson in how not to build an SST in the 1960's.