How to store gift cards on iphone

What do you mean by "store"?

For what purpose?

You can take a photo of the gift card and save it in the Photos app. That would be a way to store them.

Where do you want to store them?

What kind of gift cards are they exactly?

Some gift and loyalty gift cards may be able to be added to the Wallet App.

click here ➜ Add, use, and share boarding passes, tickets, and other passes in Apple Wallet - Apple Support

If the coffee place supports it, it may be possible to add it to the Wallet app and use it to pay through Apple Pay.

You may need to use their own app to do this.

If the coffee place does not support it, then there's no way to add it to the Wallet App.