To use a Visa gift card on Amazon, you essentially have to trick the site into thinking you're simply adding another credit or debit card onto your account, and not using as gift card at all.

If you’re really unsure of what they’re into (like when gifting something to a coworker you’re not close to), a generic Visa or Mastercard gift card does ... we don’t accept visa at ...

I received a Vanilla gift card and did not use it right away ... simple prepaid cards you can use anywhere Mastercard or Visa is accepted. They are available at many retail stores.