Is 跟他交朋友 ambiguous: can it mean both "become friends with him" and "with him, make [other] friends"?
To add a simple perspective to the other elaborated answer given, just think about the connotation to the English expression: "I made friends with him". 

In 99.9% of the time, you would know that the meaning is only two people, you and another person, who become friends. If otherwise, the context would indicate this. The same logic applies in Chinese, in this case as well as in many other semantically ambiguous situations.