How do you get the red attacks on your vivosaurs?

If you're talking about the attack choices that show up in a reddis tone at the end of the list of what each vivosaur can do, those are team attacks. The three brothers who hang out in each of the three fighter stations on each island will teach you about three different aspects of the game. The guy on Ribular teaches you how to find colored fossils so you can tell the affiliation of each fossil you dig up. The brother on Cranial teaches about dark fossils, and the last brother on Ilium teaches you about team skills. You have to fight each and win to,learn their particular skill. Once you've fought the last guy, you can put together teams of compatible vivosaurs. You can tell they're teamed up right when the dino medals have little streaks of shine going across them. When all your dinos are shining, the red team skill will show up as a choice for your action in your turn. Hope this helps.

Will you be able to do a team attack with any vivosaurs

You can also get it by fighting a lot of supper strong people like sar the last time