"Three flies up" is the name of a game of unorganized baseball. Therefore, "playing three flies up" means to play this game.
Here is a definition of "three flies up" - a simple game where either someone pitches to a hitter or the hitter just tosses the ball to himself and hits until someone in the field catches 3 pop flies. That fielder then becomes the hitter. A variation might be to give certain point totals for fielding different balls. For example 10 points for a fly ball, 5 points for a ball on one hop, 2 points for a grounder. First fielder to a certain number wins or gets to hit. This can also get as rough as you want, often turning into a hybrid of rugby and baseball depending on how much contact the fielders allow.