I would say "Don't even mix business with business with Amazon"
(not very) funnily enough, we have a business AWS account that is also used for Amazon (buying stuff for the office), as well as Amazon seller central. We've set up MFA on the AWS account, but it's in total conflict with the seller central account, which keeps asking for setting up MFA as well. If we set both, we're almost totally locked-out of our AWS. Somehow the MFA device gets mixed up or something. We can kinda squeeze-in if we try a few times with alternating between codes. Seller central seems connected to the Amazon retail, but not AWS. Totally bizarre.
We've contacted AWS MFA support several times, but there's basically no solution for this. They claim it's all somehow integrated, but something isn't quite well integrated as it should be.