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
2015-16Davis2000-01Webber1999-00O'Neal111
NAMESEASONTMGPPTSREBMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINASTSTLBLKTOVPF+/-
Anthony DavisAnthony Davis2015-16NOPNOP1592043.459.020.04.00.01.02.024.034.070.62.02.0100.09.010.090.04340121+17
Chris WebberChris Webber2000-01SACSAC1512650.051.026.05.03.02.04.024.047.051.10.01.00.03.06.050.05053244-1
Shaquille O'NealShaquille O'Neal1999-00LALLAL1612345.061.023.03.00.00.04.024.035.068.60.00.013.022.059.14530042+16
StatMuse has game-level data for rebounds going back to the 1982-83 season.