There are no direct flights from Doncaster-Sheffield Airport (DSA) to any London airport.
Sheffield-London uses the Midland Main Line, which is not a particularly fast main railway line. The fastest services take two hours and one minute.
Depending on exactly whereabouts in Sheffield you are leaving from, you might be able to use trains from DoncasterDoncaster, which use the (faster) East Coast Main Line in about 1 hour and 42 minutes.
Note that the UK Government agrees with you that Sheffield-London takes too long, and has started a programme to upgrade the Midland Main Line by 2020, which will reduce timings by about 15 minutes, and by the proposed construction of HS2, which would see trains taking about an hour from London to Sheffield after 2030.