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)
A word of caution
These types of things are prime targets for malware and zero days have been on the rise for iPhones - I would highly suggest you carefully consider whether or not this would be worth compromising your phones security over.
There are lots and lots of ways to run emulators and roms these days, including buying a handheld game kit from canakit or something similiar, I’m sure, to run retropie which could emulate any number of retro systems with negligible risk to you, your device, your accounts or your private data. Just some food for thought.