Knowledge and privilege have different spellings mostly by just serendipity and the vagaries of language drift and variation. Sometimes in language, that’s just way things are. An obsolete valid spelling of “privilege” is in fact “priviledge.”

These two words come from much different places, though. “Privilege” is from Latin by way of Old French while “knowledge” is from Old/Middle English by way of Old High German. This divergent linguistic path might have some influence because “privilege” means basically “private law” and we spell anything to do with that cognate “leg-” as found in “legal” and “legislate.” This probably helped to fix that stem it in the word “privilege.”

The above is just my speculation. Unlike most etymologists on the internet, I will admit it is such because I don’t have the time nor inclination to do all the research that’d be necessary to attempt to determine that with any degree of certainty.