Will botox or collagen injections correct a cleft chin?

Perhaps. Cleft chin is caused by the adherence of the skin in the middle of the chin to the deeper tissues. Correction requires releasing these strong attachments and placing a graft of fat or muscle to add volume. Filling agents injected under the cleft might be of some value, however, the results will be limited if the strong deep attachments are not released.
Chin correction. This can be done many different ways and sometimes requires combining methods. It is very patient dependent. A thicker filler like Radiesse (dermal fillers) and carefully placed Botox or Dysport is a good starting ground.
Filler usually. Use of fillers in cleft chin are more popular than Botox (unless muscular action is the cause-which is rare). Collegen is not used much anymore, more popular are the long-lasting types like Radiesse (dermal fillers) or artefill. Placed deep and into dermis fills effectively. Often caused by anatomy of underlying chin shape, so structural filling with fat grafts also offer help with long duration.
Prune not cleft. Botox may be used to treat a prune chin deformity (hyperactive mentalis muscle) but is not generally used for a cleft chin. Collagen is not tradtionally used for this purpose.