If you are interesting is creating an App for a membership site, we recommend checking out the BuddyBoss App.
As BuddyBoss puts it on their site:
“Launch your own WordPress powered community, membership, or online courses native mobile app”
NATIVE MOBILE APP
Your own native app, in your own Apple App store and Google Play Store accounts, with your own branding”
It appears that it allows for the creation of your own membership App (they have made that integrate with WishList Member).
The BuddyBoss team should be able to provide additional info.
More details on the BuddyBoss App.
AppMySite is another option for having an App built.