"President Trump appreciates the outpouring of support for both he and the First Lady."
Should this be he, him or himself?
"President Trump appreciates the outpouring of support for both he and the First Lady."
Should this be he, him or himself?
This is an example of hypercorrection, a mistake all too common with pronouns after prepositions in a failed effort to sound more correct.
The preposition "for" takes an object of a preposition, and the object is "him." It may seem plain or simple because it is. If you simplify the sentence to "Trump appreciates the outpouring of support for ______," this can help you tell what case the pronoun should be.
"Himself" (as a reflexive pronoun) can be used if "he" or "him" has already been used in the sentence, and is often used instead of "him" in cases like this, again, as hypercorrection. "He supports himself," for example, but not "*They support himself."