How do I login to my Instagram account on another device?
It appears you have created the Instagram account using your phone number. Snapchat account on the other hand is created with phone number.

Regain access to the original phone number from the broken iPhone. If you setup your new phone with the same number, you'll be able to recover both the account onto it. You'll simply need to install the app(s) on your new phone and authenticate via OTP received on your phone number.

You also can restore your iCloud or iTunes backup to an iPad or iPhone or possible iPod touch based on the iOS version of the backup, but you can probably work with support for each system (Snapchat, Instagram) from any mobile device with your same cell number.