I've found this on a famous forum: "I try to upgrade my iPhone 5s to the latest iOS 8, everything seems normal until the upgrades halt suddenly. And when it starts rebooting my iPhone, I found my iPhone stuck into recovery mode. After the rebooting, my iPhone was stuck in the recovery mode. I have no idea how to fix it, any suggestions?" I believe that quite a great group of iOS users have faced this issue and I will show you how to restore iCloud backup in recovery mode in the below article.
Step 1. Launch iTunes on PC and Connect iPhone to PC
Download and install the latest iTunes – iTunes 12, on your computer. After that, launch it on your PC. Connect iPhone to your computer via USB cable and you will see a pop-up window asking if you are sure you want to have your iPhone restored to factory settings or updated. Just click "Restore" to move on.
Step 2. Restore Your iPhone
Now, after the detection, click "Restore iPhone…". Then, click "Restore and Update" as you can see in the below window.
Step 3. Restore iCloud Backup
After the two steps above, your iPhone will be rebooted. Keep on to the set-up step after your iDevice successfully powered on. Just choose "Restore from iCloud Backup". Then, choose the backup file you want to restore your iPhone files from.
Note: The only pre-condition is that you should do iCloud backup with your iPhone so that you can restore iPhone data anytime you need.
Yep, that's it. After that, you can restore your iPhone data even though your iPhone is stuck into recovery mode after jailbreaking, upgrading OS, and more. It is not as complex as you think it would be, isn't it? Don't hesitate to let me know if you have any problem restoring data from iCloud even though iPhone got stuck into recovery mode.