I think it might be difficult to get a light delicate angel food texture using only nut flour (if you can use nuts), but this sponge looks like it might be your closest bet for a grain free cake that resembles angel food: https://food52.com/recipes/38114-walnut-sponge-cake
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There are plenty of recipes online for gluten-free angel food cake, none of which I have any experience with.
Just fire up your favorite Internet search engine and enter the search parameters "flourless angel food cake." You wil get pages of search results.