iOS map app that can load MBTiles tileset
I recommend you one of these :

Guru Maps, its free version allow you to load 3 offline MBTiles. Their paid version is quite expensive - 50$ but the app is well-made.
OpenMapTiles, if you want to use OpenStreetMap vectors only.
MBTiles GPS, the app interface is basic but it's free.
MapTiler Mobil‪e‬, I've never tried it but I heard great feedback about it.