[INFO/Workaround Fix] War Story Rewards Not Granted

Same happened to me and here's the way to fix it:

1. In Origin right click on BFV, then click game properties, and then on the cloud saves tab turn that off by unchecking the box and save.
2. Go to C:\Users\username\Documents\Battlefield V and move the settings folder elsewhere like your desktop.
3. Start BFV. You should be asked to change your brightness and sound settings then it will load you into the intro to war stories. Quit to the main menu as soon as you are able to.
4. Load the war story that you are having issues with. If you have a stuck challenge on the second or third mission you will need to play through until that mission. I just chose easy difficulty so I could quickly run through the missions.
5. Complete the challenge/collect the letters that were glitched for you.
6. At this point I finished out the rest of the missions in that war story. I'm not sure if this is required though. Once back at the main menu, you now should have the check mark indicating that the war story was fully completed.
7. Quit BFV. Go back to the BFV folder and delete the settings folder that the game auto generated. Then move back your old settings folder that you moved from the BFV folder earlier. Turn back on cloud saves.
8. Launch the game and go to shipments under armory and your rewards should be unlocked.

Hope this helps!