How to manage fat-gluten oxidation in celiac disease?
Gluten is a protein. The textbook answer is that protein is not stored in fat cells. 

Proteins are hydrolyzed into amino acids through digestion; some amino acids are ketogenic, and can contribute carbon towards fat biosynthesis. So some of the carbon that originates in gluten may be incorporated into a fatty acid. But the carbon has no 'memory' of its previous role in a gluten molecule, and could not act as gluten when the fat is subsequently oxidized.

One can imagine an undigested gluten molecule (or its peptide fragments) binding to the exterior of a fat cell, but there's no mechanism for it to get incorporated into fat as an intact protein.