I don’t know if anyone has thought of this but if you go in a pipe/door and it takes you to a spot above the flag pole maybe as you jump for the flag and maybe there was a way to change to a fire flower in mid air and grab the flag pole last second.

Although you don’t need a door/pipe to get to a higher position than the flag pole an example would be on 3-3 when your outside and as you jump you can maybe switch to fire flower then quickly grab it.