Can I get the Amazon Prime discount for customers if a family member receives government assistance and I use her EBT card?

I believe it's currently illegal to authorize the use of your EBT card to others not listed, whether lending or selling. Now, most states only allow one person of a household to bring in food for that address, so I understand your position. But for Amazon, it would be a lot of risk involved since someone could have had theirs stolen, which does happen a lot. What you could do is ask the person registered to the EBT card to purchase it and you can make payments to them. It may work out so both of you could split it. But yes, I believe the name of the account and credit card must match what's on the EBT card.