Well, to do that on your iPhone, you might want to try apps like Manga Storm or Manga Rock. These usually have settings where you can select and download the manga you want to read offline. Just keep in mind that the availability of certain manga might vary depending on the app and its licensing.
One way is to find manga apps that have an offline reading feature. For example, MangaZone often offers this option. Make sure to download the manga within the app when you have a good internet connection, and then you can read it offline. Also, check if the app has settings for saving manga locally.
One way to read manga offline on iOS is to subscribe to manga subscription services that allow offline downloads. For example, Comixology has a decent collection and offline reading feature. Make sure to check the app's settings for the offline download option.