After the unmarked Tommy Elphick had headed home from Eunan O’Kane’s cross to give Bournemouth a 20th-minute lead, Flynn equalised four minutes later with a close-range finish after Nick Blackman’s cross was headed down.
Flynn put United in front in the 31st minute with a low, curling shot from 12 yards out which went inside Shwan Jalal’s left-hand post.
John Cofie made it 3-1 with a superb effort on the run from outside the area two minutes before half-time. The on-loan Manchester United striker went close to repeating the feat shortly afterwards when his long-range effort struck the crossbar.
Lee Barnard met O’Kane’s corner with a firm, close-range header to give Bournemouth hope three minutes into the second half before substitute Richard Cresswell headed home Flynn’s cross to restore the Blades’ two-goal cushion on the hour mark.
However, Bournemouth would not go away and Marc Pugh drilled a low shot past Mark Howard from 25 yards in the 87th minute to put the visitors within touching distance one more, but Blackman scored from the penalty spot to seal the win in stoppage time after being brought down by Josh McQuoid.