Missing the plastic bag for shipping for my amp...

Go to home depot and get some stretch wrap or any moving supply place will have it. Comes in handy for a lot of things. 

"Guess it is just me but if you have the original box and foam inserts and the amp is resting in place between the inserts how is it going to get all scratched up without the plastic bag while in transit."

It won’t scratch it but probability of scuffing/ marring from the styrofoam constant rubbing on it.

Is it actually possible for styrofoam to permanently mark up the steel chassis of the amp?

I would go to a store like best buys or whoever and ask for the plastic bag that a computer was packaged in.

Yes those styrofoam end pieces can scuff up the finish but the suggestion of the Glad Wrap is your best bet. Manufacturers use bags because it is less time consuming and labor intensive.  If you're sending it back to manufacturer they will put it in a new bag as its faster for them.