There are clearly some problems with the flight aware data, sometimes showing a flight time of just 30m!

Anyway, according to the Beijing Airport site, the flight arrived today at 2:14am, 1h04m late.

Beijing Capital International Airport - BCIA

Generally, when you apply for a Chinese visa in a case like this you apply for a normal tourist visa, not a transit visa. Cost is the same. If you're American you should be able to get a 10-year multiple-entry visa in Hong Kong, though it will be expensive. If you're British, it will probably be a normal 30-day visa, but still expensive. Other nationalities vary.