Fletchers have the F/S record.
For F/S/S (3 generations) it is the Kennedy family. They are on 589 and counting. Josh is on 184 games. Let's say he played 270 ie. 4 more full seasons (conservative) they would make it to 675.
Silvagnis are on 551 excluding any of Jack's games (he's on 9 according to Wikipedia).
So to put it simply, assuming JPK plays four more full seasons and retires on 270, Mason or Max Fletcher would need to play 12 games to hand the Fletchers the record.
Jack Silvagni needs to play 125 games to get the record for the Silvagnis.
If he does that, Mason or Max will need to get within 113 games of him to ensure the Fletchers get the record.
Can't believe I just worked all that out...