My fiancee had kidney stone removal surgery 3 days ago, and still is in a lot of pain. Is there a complication?

Maybe. Or stone fragment still there. Can be inflammation from previous stone and the previous procedure. Call his urologist. May need to be seen.
Not necessarily . He may have stent pain, be passing a fragment or having some spasm. He should call the surgeon. For more: www.Peedoc.Com @thepeedoc.
Not necessarily. Pain after surgery is very common and sometimes the pain after kidney stone surgery is due to swelling in the ureter, the tube from the kidney to the bladder, or from an indwelling stent. Serious complications are entirely possible too unfortunately. Any pain that is not controlled by prescription medication by mouth needs an investigation from the surgeon.