A colleague made a cake for his birthday and brought it to share. He explained that it was “vegan and gluten free”. As legal editors do, we discussed whether that meant it was (vegan) and (gluten free) (probably) or (vegan free) and (gluten free) (probably not), and further what “vegan free food” might actually be (as opposed to “vegan, free food” (which would probably be “free, vegan food” anyway)).
The phrase can either be ADJ and N free or N and N free. Vegan can be a noun (My cousin is a vegan, *This cake is a vegan) or an adjective (?My cousin is vegan, This cake is vegan). Compare organic and preservative free and additive and preservative free. Hyphens might or might not help: organic and preservative-free, additive- and preservative-free, additive-free and preservative-free.
Never Pure and Rarely Simple 
To be really pedantic about this, the phrase “gluten-free” ought to have been hyphenated. And then there would be no ambiguity; no one would write “vegan- and gluten-free” unless they were being purposefully snarky.
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I can’t recall that I’ve ever written or thought about writing ‘gluten(-)free’, but I would incline to using a comma. This phrase can be used as ‘This cake is gluten(-)free’ and ‘This is a gluten(-)free cake. General Google search results for “gluten free” and “gluten-free” (in quotation marks for an exact match) are inconclusive because “an exact match” doesn’t include hyphens and the two results are mixed together. Google Ngrams shows a clear preference for “gluten-free”. I don’t think it’s pedantic to suggest using a hyphen.
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By “I would incline to using a comma” did you mean hyphen?
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Ah, yes, that thingy is called a hyphen, like I wrote in my post. Time zones and my work schedule are such that I often read your comments and reply either first thing in the morning over or just after breakfast (like my previous reply), or late in the evening, possibly after a choir rehearsal (like this one).
I completely forgot about the few months I spent as a sub-editor of magazines including supermarkets/convenience stores and pharmacies. I assume ‘gluten(-)free’ happened at least once during that time.
Today my colleague said that his solution would be to switch the order: gluten(-)free and vegan.
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