I'm playing Pokemon HeartGold on my iPhone and I love it!
I installed Ignited via SideStore. No Jailbreaking necessary. Not computer tether. SideStore can renew the side loaded emulator every 7 days when on WiFi. The iPhone is perfect for DS emulation with a stylus.
(Ignited is a fork of Delta with more options, and SideStore is a fork of AltStore, with no computer tether needed)
it's been a few years since I've used an iPhone, mainly because of the third party apps thing. Don't these usually get shut down for violating Apple's enterprise license agreement or something?