Geta means to be able to do something.  Ég get = I can. 

This meaning has nothing to do with objects.  It is an auxiliary verb.  No reflexive nor reciprocal is therefore possible. 

Even the passive is meaningless because to be able is essentially involuntary already. You cannot be accidentally able to, because that meaning is already included in the meaning of geta. If you think about it To be able to is like being granted a permission, a possibility, something that is out of our control. To do is within our control, but being able to is already passive. 

Geta is not conceivable as a state, thus: No inchoative either.