More than 35000 feet. That flight was made at 45000 feet (13700m) on October 14, 1947.
Explanation:
Most aircraft flying is achieved between 35000 and 42000 feet. At this altitude, the atmosphere still has oxygen for reaction motors to work properly and the air resistance is less compared to that of lower altitudes since the atmosphere is "thinner" there.
However, supersonic airplanes can fly at higher altitudes to avoid other slower aircraft and, most importantly, because the effects of compressibility and shock waves are less notorious after cruising the sound barrier that experiments every aircraft when and after reaching such speeds. At lower altitudes, the effects after cruising the sound barrier are increased because of the presence of more oxygen and other gases in the atmosphere.
Moreover, we have to remember that reaction motors (jet engines), such as those that most commercial and military aircraft used regularly, employ a mix of oxygen and fuel to work. The air is taken to the motor, it mixes with the fuel, and then, there is a kind of controlled explosion inside the motor and the exhausted gases impulse the aircraft that "react" to this force in the opposite direction, moving ahead the airplane at high speed.
Because of the lower air resistance, fuel consumption is also lower and we do not expect too many flying objects at this altitude, so there are also economic reasons because the aircraft can be lighter, smaller when necessary and can be constructed with more costly materials appropriate to resist those effects.
In conclusion, it is expected that supersonic flights perform at these altitudes because the oxygen and other gases are less at such altitudes, but enough to foster the aircraft engines, the fuel consumption is reduced, the effects of compressibility and shock waves are less negative, and at such speeds, it is better not to share the same space with other aircraft.
Yeager reached this on October 14, 1947, at Mach 1.05 (1.05 times the speed of sound).
