The Shulhan Aruch (Orah Haim 128:8) writes that the Kohanim must begin making their way toward the Duchan (place where they recite Birkat Kohanim) as soon as the Hazzan begins the Beracha of "Reseh." He emphasizes that regardless of when they will actually arrive at the Duchan, they must make an "Akira" – meaning, lift their feet and begin heading toward the Duchan – when the Hazzan recites the word "Reseh." A number of authorities, including the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) and the Kaf Ha'haim (Rav Yaakov Haim Sofer, 1870-1939), rule that even if a Kohen's place is at the Duchan, he must nevertheless move his feet when the Hazzan reaches "Reseh."
If a Kohen did not make an "Akira" when the Hazzan recited the word "Reseh," he may still do so until the Hazzan recites the word "Modim," at the beginning of the subsequent Beracha. So long as a Kohen left his place at some point before the Hazzan recited the word "Modim," he may participate in Birkat Kohanim. Of course, as mentioned, it is preferable for a Kohen to leave his place immediately when the Hazzan recites the word "Reseh."
Both Kohanim and Hazzanim should be aware of this Halacha. Kohanim should make a point of heading toward the front of the synagogue as soon as the Hazzan recites "Reseh," and the Hazzan, for his part, should slow the pace somewhat before reciting "Modim" to ensure that all the Kohanim make their "Akira" in time.
Kohanim generally wash their hands before going to the Duchan for Birkat Kohanim. If a Kohen suspects that if he leaves to wash his hands he will not have time to make an "Akira" before the Hazzan begins "Modim," then he should preferably begin walking toward the Duchan after the Hazzan recites "Reseh" and then go wash his hands. This way he ensures to make his "Akira" in time so that he can participate in Birkat Kohanim.
If a Kohen is still reciting the Amida when the Hazzan reaches "Reseh," he should take a small step toward the Duchan – even though he is in the middle of the Amida – and then complete the Amida and walk to the Duchan.
Summary: The Kohanim should begin walking toward the front of the synagogue for Birkat Kohanim as soon as the Hazzan begins the Beracha of "Reseh." If a Kohen did not begin walking at that point, then so long as he did so before the Hazzan began the Beracha of "Modim," he may participate in Birkat Kohanim. But if a Kohen did not begin walking toward the place of Birkat Kohanim until after the Hazzan recited the word "Modim," he may not participate in Birkat Kohanim.
