Initially the rocket was delayed for almost an hour during which time Blue Origin carried out routine safety checks.
Then the passengers on board experienced up to four minutes of weightlessness when they were blasted into sub-orbit.
The flight lasted for 11 minutes from liftoff. New Shephard safely returned back to Earth afterwards.
Mr Lei said: “It was different. I felt my skin pulling. The entire time I was in zero G I felt like I was falling to the ceiling.
“I felt a bit of nausea at one point. It was a beautiful clear day. I’m so overcome. Thank you so much.”
Bezos, the billionaire founder of online retail giant Amazon, joined on the Blue Origin’s inaugural crewed flight to the edge of space last July.
Ahead of the latest launch, Mr Allen said: “I’ve loved aviation from the time I was a kid. I used to build rockets and play with them as a kid. I always dreamed about space.”
Mr Allen said each passenger was given a small bag to take aboard with them and he chose to take a small American flag with him.
Mr Kitchen said: “Given everything that’s going on right now in the world, seeing this borderless planet from space is really important to me.”
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