I have read Wiki-pedia, the theorethical key page however does not list if there's a key signature with 6 double flats and 1 flat. The max that that page lists are key signatures with 3 double flats.
the key you're looking for IS mentioned. 6 doubles plus 1 adds up to 13 flats. It's in the list.
You could also have worked this out from first principles. C major has no flats (or sharps). C♭ major therefore has ALL the flats, 7 of them. Similarly, G♭ major has 6 flats. G♭♭ major will have those 6 plus EVERYTHING flattened again. That's 6 plus 7 flats.
I trust this information will be of great practical use to you!