Who was the last person to fly in space alone?
That all depends on your definition. The last complete solo flight (from launch to splashdown) was Gordon Cooper. Cooper's Faith 7 flight was the last Mercury flight. He launched on May 15, 1963.
On September 16, 1994, astronauts Mark Lee and Carl Meade used a chest mounted control unit called the Simplified Aid for EVA Rescue (SAFER) to fly solo in and out of the Shuttle's cargo bay. They both used the SAFER during the EVA. It is not known which astronaut used it last.
While SAFER is used on every EVA since, the last time it was actually fired in space was during flight STS-92 when astronauts Wisoff and Lopez-Alegria performed test maneuvers with it, flying up to 50 feet away from the Shuttle. They did not technically fly alone since they remained tethered to the Shuttle during the tests.