Can hanging upside down on inversion table cause my "6mm stable gallstone" (i have no symptoms from it) to move and get sucked into my biliary duct?

Anything's possible: Stones in the gallbladder (gb) seldom cause symptoms unless they migrate into the neck of the gb (& block exit of bile) or into the common bile duct. Symptomless gallstones may be diagnosed by chance by imaging or during investigation for some other condition. Bear in mind that only 10% become symptomatic within 5 years of detection.

Not likely : It is extremely unlikely that traction would be able to move a gallstone significantly whether that be by an inversion table or other technique. Traction that is applied to the musculoskeletal system would generate little if any applied force to the gall bladder, which is in a protected position in the right upper quadrant.