"When we swear an oath to support and defend the Constitution, which is a document and a set of principles and it supports the rule of law, one of those is to ensure that we do not obey illegal orders," Allen told told ABC's George Stephanopoulos on "This Week."
In the past, Trump has supported the use of waterboarding and other enhanced interrogation techniques, and has said the military should kill the families of alleged terrorists.
"He's talked about needing to torture. He's talked about needing to murder the families of alleged terrorists," Allen said. "He's talked about carpet-bombing ISIL. Who do you think is going to carpet-bombed when all that occurs? It's going to be innocent families."
Were Trump to order such things, Allen said, he would be ordering illegal actions.
"What we need to do is ensure that we don't create an environment that puts us on a track conceivably where the United States military finds itself in a civil military crisis with a commander in chief who would have us do illegal things," Allen said.