I also had the same issue. I tried everything to connect my Prime Gaming account to my EA account for two days, used different web browsers, used my mobile phone, cleared the cache, logged out and logged in, reset my router, removed all connections and reconnect, contacted with 2 EA advisors and did everything they told me to do but nothing worked. I always get the same "something went wrong" error after entering my verification code.
Then yesterday, I thought it could be a verification issue and changed my verification settings and then used another computer which I have never used before to link my accounts and it worked. Successfully linked my prime gaming to my EA account as you can see from the attached picture. Find below what I did step by step.
- Signed in ea.com and clicked account settings. Filled the empty slots at the "About Me" tab and then from the Security tab I changed my verification mode to Mobile App Authenticator. (make sure Login Verification is turned ON). A QR code generated to connect my account to the authenticator (keep the page open)
- Downloaded Google Authenticator to my android mobile phone from Play Store and added my EA account to the authenticator by scanning the QR code given at the previous step.
- Signed out from twitch, amazon gaming and EA at my computer
- Using my dad's computer which I have never used before I first signed in to twitch.tv then from the "Prime Gaming Loot" section up right I choosed FIFA 21: Prime Gaming Pack (you can select another Electronic Arts game loot). It took me to Prime Gaming web site and I signed in. Clicked the "Claim Now" button on the loot and a small window popped up, and then clicked "Go To EA" button from the "Link Game Account" section below. (If you have already claimed the loot then "link game account" section won't be show up, in this case you can claim any other Electronic Arts game loot that you haven't claimed before to show it up)
- I was redirected to the EA Account sign-in page and I signed in with my ID and password. Asked me the verification method and I choosed Google Authenticator instead of my e-mail.
- Opened Google Authenticator and a six digit code was created, typed this code to my EA verification page opened in the previous step.
- A menu popped up and there I allowed EA to access my Prime Gaming membership.
- Was ready to see "something went wrong" message but this time it worked and accounts succesfully linked.
I solved my problem after all, and hope this will work for you too.