How to fix: stuck in a repeated loop using Transfer Directly from iPhone when setting up new iPhone
If you are setting up a new iPhone, and you wish to transfer all of the data from your older iPhone to the newer iPhone wirelessly via Bluetooth, it is important that both iPhones be running the latest version of iOS before you begin this procedure. If they do not have matching iOS versions, then upon approaching the older iPhone to the newer iPhone on the Hello Quick Start screen, the iPhones will detect each other, you will position the blue hologram circle in the camera of the other iPhone, followed by setting up Touch ID and Create a Passcode. Unfortunately, once you reach the Apps & Data screen, selecting Transfer Directly from iPhone will return the user to the Hello Quick Start screen, creating an endless loop where the wireless data transfer will never begin.
It is highly recommended that when either updating any device or when transferring data wirelessly, that the devices in question be connected to a power source such as an AC adapter wall plug.
With an Internet connection established on the iPhone(s), checking for iOS updates (and updating as necessary) can be performed by selecting SETTINGS - GENERAL - UPDATE. If you are not sure if the newer iPhone is up to date and you are stuck on the Hello Quick Start screen, temporarily choose the following options: SET UP MANUALLY - SET UP TOUCH ID LATER - PASSCODE OPTIONS (DO NOT USE PASSCODE) - DON'T TRANSFER APPS & DATA. Once you arrive at the iOS interface, ensure that an Internet connection is established on said device and then tap SETTINGS - GENERAL - UPDATE. Once the newer iPhone iOS is up to date, to return to the initial device set up (factory data reset as it is known on other devices) tap SETTINGS - GENERAL - RESET - ERASE ALL CONTENT AND SETTINGS and then begin the wireless transfer procedure once again.