My daughter loves aerial silks and wants to do it more often. We would like to hang the silks from a tree branch. Is that possible? We want it to be safe.

Depends on what kinds of trees, health of tree, how you attach to the branch, etc. A safer approach might be to attach a cable between two large, healthy tree trunks, using large eyebolts and multiple cable clamps.
Or, use lumber bolted to one trunk with well-designed support braces either supporting the horizontal member from below or above.
I vote no for just hanging it from a branch.

How old is your daughter? My vote is to get her involved in actual lessons versus do it at home.