Twin packs can be obtained from the tournament, or they can be bought from the in-game app purchase shop.
Depending on how high you got in the tournament, the reward will differ. For example, finish in the "Survivor" league and you will get the "Rare Twins" pack.
Rare Twin Card Pack
Legendary Twin Card Pack
The best Twin Packs in the game right now would be the "Legendary Twins". They consist of two Legendary dinosaurs as a reward for finishing in the "Predator League."
Tips to get them: If you don't participate in the tournament with effort, you would almost have no chance of getting them. At least take your time and effort. Especially for early game, just ending up in the survivor league would give you a lvl 20 rare! That is very decent. So use the tournament to your advantage so you can get dinosaurs easier.