TT #31 · Parshas Shemini · Aliyah 2 · Passuk 22
Chabad.org — English translation + Rashi
English: “He descended from making the sin-offering”: because Aaron blessed the people before descending, the Sages established the priestly blessing after the blessing of thanksgiving.
Megillah 18a.
E-Daf.com — Megillah 18a (Tsurras Hadaf)
Textual inference — the juxtaposition of Aaron’s blessing with his descent from the altar establishes the placement of the priestly blessing after the thanksgiving blessing.
The sequence of Aaron's blessing immediately after his sacrificial service provides the basis for placing Birkat Kohanim after the blessing of thanksgiving in the Amidah.