Transfering MR points to Avios is a very simple process. Here’s how:
Log into American Express, tap on “Use Your Points” then in the search bar search for British Airways Executive Club. You’ll be presented with the above page as you won’t have a BA account linked. Tap on Add another account.
This is where you’ll link your Executive Club account to your AmEx account. For this, you’ll need your 8 digit British Airways Executive Club membership number which you can find in your BA account. Once you enter all the above information your account is linked right away.
Now that you have your BAEC account linked to AmEx you can transfer points. Every 1 AmEx Membership Reward point equals 1 Avios. In VERY VERY rare times (think bi-annually), there are promotions where you can transfer with a 10-30% bonus making 1 MR point 1.3 Avios. You have to transfer at least 1,000 MR points and they have to be in multiples of 500. So 20,000 is okay, 20,200 is not okay.
The final step where American Express clearly warn you that once you make the transfer you can’t go back. American Express also states it takes 3 days for the process to complete, I’d ignore that. Based on my experience it takes just a few hours before the Avios show in your BA account.