To get monthly free loot boxes, all you need to do is link your Blizzard account to your Prime Gaming account. Go to the Prime Gaming Overwatch page and click Link Account. You will then be directed to Blizzard’s website, where you will need to sign in to the Battle.Net account that you use. If you are playing on a console, this is the same account you use to access crossplay functionality.
After you have successfully signed in, simply click claim under the loot box, and the next time you log in to Overwatch, you will have that tiered box waiting for you. Between March and September, there will be one loot box made available to you for either standard or legendary loot boxes; the latter have at least one guaranteed legendary item inside. You will need to return to the Prime Gaming page to redeem it each month.