This answer was given before the class of the pc in question was known. So far it was assumed to be hunter.
For a druid's companion pack flanking is hard (if at all possible) to get and without it the outflank + paired opportunities combo doesn't work.
A strong combo for Master and animal companion is Outflank +
Pack Flanking + Paired Opportunists, because it allows you
to fight side by side and flank at the same time. Also, if one of the
duo scores a critical hit both get an AoO.
It works like this: Pack Flanking allows you to flank while fighting
side by side. Outflank gives the ally an AoO if the other one scores a
crit and Paired Opportunists lets you make an AoO if your ally can
In addition, your flanking bonus increases to +4 (Outflank) and all
AoOs get a to hit bonus of +4 (Paired Opportunists).
I played a hunter wielding a scimitar (a high threat weapon) with a
Stegosaurus animal companion (single high damage attack similar to the
T-Rex) but with a higher Dex. The animal companion also had Combat
Reflexes, which my hunter lacked. Later in the campaign, I found a
keen scimitar which allowed me to get more crits and thus generate more AoOs. All in all, I found this combo very strong but it would be
less so without Combat Reflexes on the animal companion or with a low
threat weapon on the character.
I did not want to outright delete the previous answer that was, more or less, invalidated by the change of question so I decided to mark it with the blockquote and the preceding disclaimer.
For a druid/T-Rex combo there are few teamwork feats that increase damage directly. There is precise strike (if you fulfil the dex requirement) but it is not multiplied for vital strike and thus better for lots of weak attack than for single strong ones.
Escape route makes it easier to reach a flanking position without provoking AoOs so it COULD be seen as an indirect damage increase but all in all it is more a defensive feat.
There are some feats which can be used to increase damage but most are hard to qualify for with the animal companion. This includes the ones mentioned in the original answer and others like broken wing gambit.