This was of particular interest to the U.S. Navy because of the need to minimize the approach speed of carrier-based jet airplanes. In 1951 a Navy engineer suggested using the problem as part of the solution, with the jet engine compressor being a convenient source of the air required.A test program resulted a few years later with a modified F9F Panther. At-sea carrier trials in 1954 demonstrated a significant reduction in approach speed, 10 to 15 knots depending on weight, which was limited by inadequate roll control at the lower speed rather than stall.
As a result, BLC was incorporated on a few US Navy airplanes in the late 1950s, although its first usage may have been in the Lockheed F-104 Starfighter which first flew in 1954. Like most gadgets, it was a mixed blessing. In at least two cases, the F4H Phantom and the F-8 Crusader (French and F-8J), it was an addition to an existing design to accommodate a necessary increase in gross weight. It might have been in the A3J Vigilante design from the beginning because the Navy wanted to be able to launch its long-range nuclear strike aircraft with no wind-over-deck at all. It also appears to have been in the F8U-3 from the beginning, Vought engineering having a penchant for incorporating this sort of thing, and the Blackburn Buccaneer. Note that all these were carrier-based airplanes, for which low-speed lift was far more important than land-based counterparts. However, as noted above, the F-104 incorporated BLC to compensate for its tiny wing and TSR2 did as well, because of its need for a high wing loading for high-speed low-level flight combined with a reasonable takeoff and landing distance.
This is a photo of the French F-8 flap system ducting taken and annotated by Tom Weinel:
Although it provided more lift at a given speed or the same lift at a lower speed as a non-blown wing, BLC was a maintenance burden, increased weight and complexity/cost, and robbed the engine of thrust on a wave off and takeoff. Troublesome failure modes included the fire hazard of a leak of the hot air in the ducting and a roll control problem on takeoff or landing if one side or the other failed to provide air for some reason. My guess is the overall experience in the 1960s resulted in BLC being infrequently taken out of the designer's tool box thereafter. The only current application that I can think of offhand is the Japanese ShinMaywa seaplane, which needs to take off and land at extremely low speeds in order to land in relatively high sea states in open water for at-sea rescue. In this case, the BLC air is taken from a compressor driven by a fifth and small turboshaft engine.