Anthony Davis, Chris Webber and Shaquille O'Neal are tied for the most games with 50+ points and 20+ rebounds in a season, with 1 game.

most games with 50 points 20 rebounds in a season
Interpreted as:
most games by a player with 50 or more points 20 or more rebounds in a season
Anthony DavisAnthony Davis2015-16NOPNOP1592043.459.
Chris WebberChris Webber2000-01SACSAC1512650.
Shaquille O'NealShaquille O'Neal1999-00LALLAL1612345.
StatMuse has game-level data for rebounds going back to the 1982-83 season.