Jai Ho might be considered a patriotic song by certain quarters, due to its prevalence in Indian culture - it has also been popularized after Western artists recorded their own version too.
The actual phrase 'Jai ho" simply means let victory prevail in Hindi.
So while you can see how that might apply to national spirit and patriotism, especially in a military sense, the actual phrase and song doesn't have any specific ties to Indian patriotism.
Instead, I would suggest any of these following patriotic songs if you wish to enjoy such things and celebrate India's great culture:
Maa Tujhe SalaamAisa Desh Hai MeraAe Mere Watan Ke LogonSarfaroshi Ki Tamanna
