Is it theoretically possible to treat filaggrin deficiency with a dietary supplement?
I highly doubt it. Filaggrin is a human protein which is expressed in the skin and stored as profilaggrin. The profilaggrin has a molecular weight of about 350 kDa (which is rather big) and is cut into smaller units of filaggrin, which then crosslinks kreatin fibers of the epidermal keratinocytes. This enhances the durability of the skin. Mutations in the filaggrin gene have been associated with dry skin and excema. See here for more information:"Filaggrin - revisited."

To supplement the profilaggrin, you would have to bring this rather large protein into the skin. You could think about making a cream with the smaller filaggrin in it to promote crosslinking of the upper skin. The question here would be how effective such a treatment ist and how deep the crosslinking would be.