What are key indicators that my kidney stone has passed and left my body?

No more pain: I assume you did not see it pass (by straining your urine). If not, if the pain is gone, the stone likely has passed although it may be in the bladder and still need to go through the urethra. A urinalysis could detect blood in the urine if the stone is still lodged in the ureter.

Stone in the toilet: If you see a kidney stone pass accompanied by relief of your pain, the storm has probably passed. Sometimes fragments or multiple stones will pass and radiographic evaluation is indicated to ensure that no clinically significant fragments remain in the kidney, ureters or bladder after passing stone material in the urine.