The Blackbird wouldn't have been a very good platform for orbital launching. The D-21 launches were actually conducted with a purpose built A-12 Blackbird (the original aircraft the SR-71 was derived from) called the M-12 (also called M-21). It had a launch control station in back behind the pilot (where an RSO would sit in an SR-71).During testing of the D-21, originally the drone was fitted with a frangible aerodynamic nose shroud, designed to blow off and disintegrate to reveal the drone's ram jet inlet to the air at speed. First time they tried to jettison the cone though, the pieces damaged the drone big time.
Option 2 had the drone operational prior to the launch attempt as drag from the drone made the combination a real gas hog as the jet accelerated a bit slowly. So the D-21 was fired up and used as an additional engine to accelerate the combination to mach 3 with the D-21 getting its tanks topped off from the Blackbird's fuel tanks.
To make a long story short, several separation tests were done with unpowered D-21s and they were successful. One successful air launch of a powered D-21 was made. But on the second attempt, the D-21 collided with the mothership and it caused the Blackbird to pitch up and breakup. Both crewmembers ejected, but one drowned because he got injured in the ejection and was unable to pull himself into his liferaft. After that, Kelly Johnson scrapped the project and all operational D-21 drone launches were done with a modified B-52H and a rocket booster designed to get the drone up to speed for the ram jet to work.
As an addendum to that program, a NASA operated SR-71 was fitted with a special pod containing a test version of Lockheed's Linear Aerospike motor for the X-33 program. Called LASRE (Linear Aerospike SR Experiment), the idea originally was to fire the motor at speed and measure the performance. But the pod incurred a substantial drag penalty on the Blackbird and after the pod was built, somebody realized it might not be smart to have liquid hydrogen and oxygen tankage that close to a "hot" aircraft structure as a Blackbird travelling supersonic does generate a fair amount of heat. So the only operational flight test of LASRE was a cold flow test with helium (it was successful).
As such, launching a craft at Mach 3 doesn't offer much benefit compared to just dropping it from an aircraft at altitude as the drop adds a little speed, altitude means thinner air to fly through and a rocket booster can do the rest. The D-21 showed that with its operational drops from a B-52H and years later the Pegasus booster showed a payload could be launched into orbit that way (admittedly small and not manned, but the method could be scaled up). If Blackstar really did fly, I imagine it had similar challenges to what the D-21 program had, but dropping a craft is potentially a lot easier then sending one up off its back.