What part of Amazon Prime are you wanting to share? Ability to get free shipping or PrimeVideo?
For shipping, I allow my son to make purchases and have them shipped to his address, he reimburses me for the cost of the product. For my daughter, she tells me what she wants and sends me the cash, then I place the order. I have both kids addresses saved in my account. My kids are very different and although I am not concerned about my son being able to order gods on my account, for my dd, I have to ask for cash upfront. She understands why and it works for us.
I just checked with my PrimeVideo account and I can register other devices to use it. I do not know how many.