Are you talking AFL + SANFL?? If so be careful because we finished 2nd a few times as well as won the flag and there were no grand finals. The first regular GF was 1898. See
https://web.archive.org/web/20100615214830/http://fullpointsfooty.net/sanfl_part_1.htm
We won 20 GFs at Adelaide oval and won the league 3 times when there were no GFs in 1884, 1890 and 1897, we won 13 GF's at Footy Park and 1 at the MCG.
We finished 2nd with no GF's in 1883, 1888, 1891, 1892 and need a "grand final" game in 1889 to separate us from Norwood as we both won the same number of games and lost that year and needed a decider game.
We lost 25 GF's at AO
http://australianfootball.com/articles/view/Adelaide+Oval+Grand+Finals+1898-1973/339
1898 South Adelaide 8.8 d Port Adelaide 4.8 7,000
1901 Norwood 4.9 d Port Adelaide 4.5 6,500
1904† Norwood 9.8 d Port Adelaide 8.10 11,000
1905 North Adelaide 6.8 d Port Adelaide 1.6 10,500
1911 West Adelaide 7.9 d Port Adelaide 6.10 19,000
1912 West Adelaide 6.10 d Port Adelaide 5.2 28,500
1915 Sturt 6.10 d Port Adelaide 4.10 13,000
1925 Norwood 8.4 d West Torrens 7.9 37,750
1926 Sturt 9.10 d North Adelaide 8.10 30,000
1927 West Adelaide 10.11 d North Adelaide 8.10 33,222
1929 Norwood 16.14 d Port Adelaide 10.9 35,504
1930 North Adelaide 9.13 d Port Adelaide 9.9 23,609
1931 North Adelaide 17.13 d Sturt 11.11 34,202
1934 Glenelg 18.15 d Port Adelaide 16.18 30,045
1935 South Adelaide 15.9 d Port Adelaide 13.13 26,496
1938 South Adelaide 23.14 d Port Adelaide 15.16 33,364
1945 West Torrens 15.25 d Port Adelaide 15.12 47,500
1946 Norwood 13.14 d Port Adelaide 9.10 53,473
1953 West Torrens 9.13 d Port Adelaide 8.12 42,949
1964 South Adelaide 9.15 d Port Adelaide 5.12 56,353
1966 Sturt 16.16 d Port Adelaide 8.8 59,417
1967 Sturt 13.10 d Port Adelaide 10.17 58,849
1968 Sturt 12.18 d Port Adelaide 9.9 57,811
1971 North Adelaide 10.19 d Port Adelaide 9.5 52,228
1972 North Adelaide 19.14 d Port Adelaide 10.12 55,709
We lost 1976, 1984 and 1997 at Footy Park.
So I make we have won 20+13+1 = 34 vs lost 25+3+1 = 29 with a good argument that you add 1889 to make it 30.