Is it possible to somehow get Channel Smite on a Fighter? How does one get a Healing Font as a Fighter, which Cleric feat would do it?
The short answer: you don't
The long answer:
Only with cleric as main class you get the divine font that opens up channel smite. The only way to be a full fledged fighter with Channel smite would be dual classing. If you table does not play with that you either become a warpriest doctrine cleric or a clerit that gets the dedication for fighter.
The last option would that you talk with you gm if they houserule something that helps you out.