How long does it take for someone to receive a gift card by email?

I would think it would be only a matter of a minute or so since it is likely all automated. Have you checked your junk mail? You can try re-sending it.

Resend iTunes Gifts - https://support.apple.com/HT201783#resend - "If you sent an iTunes Gift and your recipient can't find the link to redeem it, you can resend them the gift from your iPhone, iPad, or iPod touch or your computer. When you resend an iTunes Gift, the recipient will receive another email with a link to redeem the gift."