Upvote:1
You can take the TK flight from Mumbai(TK721) to Istanbul to Sao Paulo or Buenos Aires (TK 15). There's a flight from Delhi too, if that's more convenient for you. Turkey does not require any transit visa.
Upvote:2
A reasonable routing to get from India to Jamaica would be via either Istanbul, Paris, or Amsterdam to Panama City, and thence to Montego Bay or Kingston. Neither Panama, Turkey, the Netherlands, nor France require airport transit visas for Indian citizens.
Upvote:4
You cannot transit through airports in the Czech republic, Germany, Spain or the UK. The rest of Europe is fine though
Another option would be going via East Asia and flying from there to South America (India-Japan-Mexico-Jamaica for example). Japan and Mexico don't require transit visas for changing flights (without going through passport control)