The calculated distance (air line) between Stuttgart and Kempten (Allgäu) is approximately 90 miles respectively 144 kilometers.
By car or train, the actual journey to Kempten (Allgäu) is certainly longer, as only the direct route (as the crow flies) between Stuttgart and Kempten (Allgäu) has been calculated here.
Air line (approximately)
144 kilometers
78 nautical miles