Comment by lo_zamoyski

If he looks sick, that might be enough to nudge him in the right direction, in private. "Are you okay? You really don't look well. Having worked in a GI wing at a hospital, I've noticed a few signs that might point to serious GI issues. I would suggest you see a doctor ASAP, just to be safe." If he asks what signs, you can say "among others, you look ill". That way, you can avoid talking about the smell. You can also say you don't feel comfortable getting into the details, but that you nonetheless felt morally bound to let him know based on your experience.

Or perhaps mention it to your manager. He can then tell your coworker that there has been concern about his health and that he recommends seeing a specialist.

What he does with that information is completely his responsibility after that. You cannot make anyone happy by force, and it isn't any of your business.