It appears in the Mishnah Berura, as well as Aruch HaShulchan, Orach Chaim 274: וכן מותר ליתן גרגיר של מלח וגריס של פול על פי הנר בערב שבת כדי שיהא דולק יפה בשבת, "And it is permissible to put a grain of salt and a grain of bean by the candle on the eve of Shabbat so that it will be well lit on Shabbat." How does this adage fit with reality? Moreover, I asked an expert that produces oil candles who claimed that it is not recommended to add salt because it might impair the quality of the illumination?
The MB and the AHS both get it ultimately from Tosefta, Shabbos 2:6.
Rashi (Shabbos 67b, s.v. בול) says that putting a block of salt in the lamp "clarifies the oil so that it will be drawn into the wick." So it's not talking about mixing salt into the oil (which is probably what your expert was talking about), but about putting a chunk of it there.
Mishnat Harambam (note לא) comments that "the salt prevents the oil from getting cloudy," maybe because impurities in the oil are adsorbed onto its surface, and "the bean prevents the oil from catching fire all at once," maybe because of its high water content.