Do they accept Disney gift cards here for payment. Do they have their own gift cards also?

Hi Sabrina, thanks for reaching out! We do accept Disney gift cards as a form of payment, just not Disney Dine cards. Also, we have our own gift cards available in-store only. We’re currently running a promotion from Nov. 23, 2018 to Dec. 25, 2018, for every $100 gift card you purchase, you'll receive a bonus $20 gift card to use on a future visit. More information available at http://www.fronteracocina.com/events/.

Yes, they accept gift cards

I would definitely call, but it is on Disney property, so i would think so?

Don't know. Contact Disney relations. They would have the answer for you