He won't reach that speed.
Based on wind resistance, the terminal velocity of a skydiver in a belly-to-earth (ie:face down) free-fall position is about 122 mph.
This velocity is the limiting value of the acceleration process because the effective forces on the body balance each other more and more closely as the terminal velocity is approached.
In this example, a speed of 50% of terminal velocity is reached after only about 3 seconds, while it takes 8 seconds to reach 90%, 15 seconds to reach 99% and so on.
Higher speeds can be attained if the skydiver pulls in his or her limbs. In this case, the terminal velocity increases to about 200 mph which is almost the terminal velocity of the Peregrine Falcon diving down on its prey.
The same terminal velocity is reached for a typical .30-06 bullet dropping downwards—when it is returning to earth having been fired upwards or dropped from a tower—according to a 1920 U.S. Army Ordnance study.
Competition speed skydivers fly in the head down position and reach even higher speeds. The current world record is 614 mph by Joseph Kittinger, set at high altitude where the lesser density of the atmosphere decreased drag.
So this guy hopes to break the current world record by 76 mph? The physics don't support it.
And if he does, as you say, he's dead meat.
Show me how the physics don't support it. I did the math, and the physics seem to support it on this end. Given that terminal velocity of an object increases by 1% for approx every 160m of altitude he's on more than safe ground.
He's giving himself almost 12,000m more elevation than the previous record holder used to set the record. That's not only a substantial increase in time to accelerate, but it will occur in an atmosphere with markedly less friction to boot. He should be close to the old record by the time he reaches the altitude that attempt started at. He's still going to have a good 10,000m after that before resistance becomes the greater force and he begins to scrub speed.
Which bring up another concern: Parachute aside, he's going to start slowing down a lot once he enters the troposphere, and that energy has to go somewhere, and it will. He's going to heat up. All that kinetic energy is going to be converted into heat.