It's commonly known that non Kohanim shouldn't look at a kohens hands during Birchas Kohanim. What is the source for this?
This idea is brought down in Shulchan Aruch Orach Chaim 128:23:
בשעה שהכהנים מברכים העם לא יביטו ולא יסיחו דעתם אלא יהיו עיניהם כלפי מטה כמו שעומד בתפלה והעם יכוונו לברכה ויהיו פניהם כנגד פני הכהנים ולא יסתכלו בהם: הגה וגם הכהנים לא יסתכלו בידיהם על כן נהגו לשלשל הטלית על פניהם וידיהם חוץ לטלית ויש מקומות שנהגו שידיהם בפנים מן הטלית שלא יסתכלו העם בהם (ב"י): At the time that the kohanim bless the congregation, they should not glance [around] nor get distracted; rather, their eyes should face downward in the same way one stands in prayer. The congregation should be attentive to the blessing, and their faces should face the kohanim, but they should not stare at them. [Ram"a: And the kohanim should also not stare at their own hands; therefore, it is customary for them to wrap their tallis on their faces and keep their hands outside the tallis. And there are some places where they have the custom that their hands are kept within the tallis, so that the congregation does not stare at them (Bet Yosef).]
See the Mishnah Berurah (89) there who writes that there is no real prohibition to 'see' the Kohanim nowadays, but rather the prohibition is against 'staring' in a manner that distracts the listener. However, in the times of the Bais Hamikdash, it was prohibited to even look at the Kohanim during Birchas Kohanim, since Hashem's Shechinah was 'resting' on their hands at that time.