Hi Liz. I just Googled "gluten free restaurants Tenerife" and found a page on TripAdvisor listing the best gluten free restaurants on the island. You can check it out yourself here:
https://www.tripadvisor.co.uk/Restaurants-g187479-zfz10992-Tenerife_Canary_Islands.html#EATERY_OVERVIEW_BOX