After Ian Cox had headed a first-half opener, Flynn netted with two strikes at the start of the second before Vale fought back late in the game.
With both sides assured of their League One status for next season, the game had a distinct end-of-season feel to it early on, with Gillingham enjoying the better of the opening exchanges.
Skipper Flynn and Gary Mulligan both missed the target early on when well placed, while Danny Spiller also saw a shot blocked after wriggling free from a posse of defenders.
Vale gradually began to enjoy some possession, but as half-time approached they fell behind to a simple set-piece.
Nicky Southall whipped in a precise corner and centre-back Ian Cox rose to power a bullet header past Vale keeper Joe Anyon.
The Valiants thought they were back on level terms a minute before the interval but Akpo Sodje was adjudged to have fouled debutant keeper Simon Royce as he headed home Luke Rodgers' cross.
Vale were again nearly punished in first-half injury-time, but Spiller blazed over from six yards out despite having time to control Danny Jackman's centre.
That miss was forgotten in the 49th minute as Flynn took advantage of some slack marking to meet Clint Easton's cross with a firm header that found the roof of the net.
Four minutes later the skipper was on the score-sheet again, bending a 25-yard free-kick around the wall past the bemused Anyon.
Perhaps determined to salvage some pride, Vale came back fighting and on 77 minutes Royce denied Rodgers with a point-blank stop.
But the keeper was helpless to prevent Danny Whitaker's volley a minute later that screamed into the corner of the net.
Vale continued to push and took further gloss off Gillingham's win when Leon Constantine converted a penalty in added time after Ben Chorley had felled Rodgers in the area.