I think as long as Flat Stanley does not have any words on him they might. They can not hold signs or items with words I think because Disney does not want it to appear that the characters are supporting or endorsing anything. As long as Flat Stanley is just a paper "kid", that may be okay. I know I have seen pictures of characters holding him before.
If they say no, you could find a way to hold it where you can crop the other person out later. I know Mickey has taken pictures with DD where they are each holding the hand of a stuffed animal and it is between them.
I've also had a character hilariously "throw" DD out of picture to have its picture taken just with her stuffed animal.