I once sent an email to food scientist Harold McGee asking something similar. I have a wood oven and wanted to know if I could safely bake a gluten free pizza in there before cooking wheat based pizzas. My thought was that the oven heating process would turn any residual flour into ash. Here's the question part of what I wrote:
So here's my question: at what temperature would high gluten pizza flour burn up and no longer contain gluten? The oven would be heated up to a minimum of 600 degrees F and often hotter depending on the style of pizza I'm making. My thought is that if I fired the wood oven hot enough and long enough, any residual flour on the oven floor would become gluten free ash. If I cooked a few gluten free pizzas before making traditional pizzas using a separate, gluten free pizza peel they could enjoy a wood fired pizza too. If you think the risk of cross contamination would still be present, I'll move ahead with just the separate, gluten free propane pizza oven plan. It pains me to see the frozen gluten free pizza they eat at parties. I'd like to change that this summer.
And here's his answer:
About gluten: it does seem reasonable that temperatures high enough to char flour would completely eliminate the immunological reactivity of gluten. But I've been unable to find any studies that have actually demonstrated it. And I suppose it's remotely possible that some flour aggregates could char on the outside while insulating the interior. If you go ahead with one oven, I would just be sure to give it plenty of time to mineralize any residues from the last batch.
I took that as there were no guarantees the gluten would be completely gone. So what I did was buy a Blackstone on closeout and I keep it gluten free. My concern was that something would get in between the bricks on the floor and somehow cross contaminate the gluten free pizza. The celiacs I know aren't getting sick on my watch. It might be different in an Ooni. Never cooked in one but I think the floor is a solid piece.