Elgin Baylor had the most games in the NBA Finals with 30+ points and 10+ rebounds, with 19 games.

most games in finals with a 30 point and 10 rebounds by a player
Interpreted as:
most games in finals with a 30 or more point and 10 or more rebounds by a player
BaylorJamesO'NealPettitAbdul-JabbarOlajuwonHavlicekWestChamberlainHaganHeinsohnAntetokounmpoDurantDuncanJordanBirdBarryRussellButlerLeonardWadeMaloneBarkleyMcHaleJohnson191616141165444433333332222222
NAMESERIESGPPTSREBMPGPPGRPGAPGSPGBPGTPGFGMFGAFG%3PM3PA3P%FTMFTAFT%MINASTSTLBLKTOVPF+/-
Elgin BaylorElgin BaylorNBA Finals1969230145.136.415.813.329.245.69.812.280.285661
LeBron JamesLeBron JamesNBA Finals1657619744.236.012.37.81.91.13.313.627.349.92.86.641.56.08.273.370712530175336+65
Shaquille O'NealShaquille O'NealNBA Finals1658423844.436.514.93.30.62.13.114.323.361.10.00.08.015.352.2711529334953+51
Bob PettitBob PettitNBA Finals1448725943.934.818.511.825.845.711.213.881.361549
Kareem Abdul-JabbarKareem Abdul-JabbarNBA Finals1137715543.334.314.14.40.53.43.314.826.256.60.00.04.66.275.0476485342041
Hakeem OlajuwonHakeem OlajuwonNBA Finals61957643.232.512.73.71.73.22.713.526.550.90.20.2100.05.37.571.12592210191626
John HavlicekJohn HavlicekNBA Finals51855748.837.011.46.413.226.450.010.611.691.42443220
Jerry WestJerry WestNBA Finals41594546.039.811.36.813.025.551.013.817.379.71842710
Wilt ChamberlainWilt ChamberlainNBA Finals414210446.035.526.03.315.326.058.75.011.842.61841310
Cliff HaganCliff HaganNBA Finals41465542.336.513.84.312.823.554.311.012.886.31691717
Tom HeinsohnTom HeinsohnNBA Finals41365839.334.014.53.013.827.550.06.510.363.41571218
Giannis AntetokounmpoGiannis AntetokounmpoNBA Finals31333940.144.313.04.00.72.73.315.023.364.30.73.320.013.718.075.91201228108+33
Kevin DurantKevin DurantNBA Finals31083742.436.012.35.32.02.34.313.723.059.44.37.756.54.34.3100.012716671312+13
Tim DuncanTim DuncanNBA Finals3955344.131.717.72.72.03.01.312.319.762.70.00.07.09.772.413286946+38
Michael JordanMichael JordanNBA Finals31193643.039.712.07.31.70.33.714.730.348.41.32.750.09.012.075.01292251116+15
Larry BirdLarry BirdNBA Finals3944142.331.313.73.01.31.34.711.321.752.31.02.050.07.78.788.5127944148
Rick BarryRick BarryNBA Finals31213241.040.310.72.715.337.740.79.713.074.4123812
Bill RussellBill RussellNBA Finals39210649.730.735.33.710.019.351.710.713.778.0149119
Jimmy ButlerJimmy ButlerNBA Finals2752346.037.511.512.03.51.54.012.519.564.10.51.533.312.013.092.392247382+25
Kawhi LeonardKawhi LeonardNBA Finals2702639.635.013.02.52.51.02.59.521.045.23.59.038.912.512.5100.07955255-1
Dwyane WadeDwyane WadeNBA Finals2782344.239.011.53.53.01.53.012.022.054.50.51.050.014.519.574.48876369+15
Karl MaloneKarl MaloneNBA Finals2682142.534.010.55.02.50.03.513.024.054.20.00.08.010.576.285105076+13
Charles BarkleyCharles BarkleyNBA Finals2742546.037.012.57.02.01.01.513.022.557.80.01.50.011.013.581.592144234
Kevin McHaleKevin McHaleNBA Finals2632639.031.513.01.51.01.53.010.515.567.70.00.010.512.584.078323610
Magic JohnsonMagic JohnsonNBA Finals2742645.037.013.08.02.00.53.013.020.563.40.00.50.011.011.0100.090164163
StatMuse has game-level data for rebounds going back to the 1956 Finals.