Some random notes I cribbed together regarding GSM feature codes on the iPhone on the AT&T network. I tried some of them (including the #31# trick), but not all of them. YMMV.
GSM Feature Codes (that appear to work on the iPhone on AT&T)
Feature codes 21, 67, 61, 62 appear to work. Note changing the number for unanswered voice calls from the default that was plugged into the phone may make it harder to reset; meaning if you set up call forwarding to something other than the voice mail number (on my phone 1-253-709-4040), write down what was was before so you can re-enable voice mail.
Feature code 31 appears to work. (#31#number hides your phone number.)
All codes work. The two digit call values all accept the same formats documented in the link above, I believe. (Note that some of these codes duplicate functionality that can be found in settings.)
This notes that you can also set a timeout parameter for “Forward if not answered” so as to set the amount of time before your call forwards somewhere. I don’t know if this works. Note that the FIDO code (3436) to send to voice mail doesn’t appear to work on the iPhone. Typing in a 10-digit number (starting with 1 + area code + number) appears to work.