There is indeed a possibility for a kohen to go up for Birkat Kohanim while in the middle of Shemoneh Esrei, but there are limitations as well.
The Radbaz[2] says that if there is no other kohen who will be doing Birkat Kohanim, then a kohen who is still in the midst of Shemoneh Esrei should interrupt his tefilla to go up and do it. The Radbaz asserts that since Birkat Kohanim is a mitzva from the Torah – as opposed to specific tefilla sections, which are Rabbinic – the kohen’s obligation in Birkat Kohanim takes precedence. The precedent for this is the halacha that when a kohen serves as a chazan, he can recite Birkat Kohanim if he is able to effectively return to his tefilla afterward.[3] If, on the other hand, there are other kohanim in the congregation, there is no need to disrupt one’s Shemoneh Esrei. Although a kohen has a personal obligation to duchen, that obligation is activated only when he is called upon to do so.[4] The Radbaz posits that when the call to the kohanim to recite Birkat Kohanim is made, it is addressed only to those who are available, which usually does not include those still in the midst of Shemoneh Esrei. The Magen Avraham[5] remarks that if an individual kohen who is still davening was specifically told to go up for Birkat Kohanim, his obligation would indeed be activated, and he would have to stop his tefilla and fulfill it.
There are restrictions, however, on a kohen’s ability to interrupt his tefilla in order to go up for Birkat Kohanim. In order to do so, one requirement is that the kohen must move at least slightly in the direction of the place of Birkat Kohanim during the beracha of R’tzei.[6] Another is that this break will not preclude his ability to resume Shemoneh Esrei properly afterward.[7]
The Mishna Berura,[8] after citing the Magen Avraham, brings other significant opinions[9] that question, considering the strictness with which Chazal treated Shemoneh Esrei, whether it is permitted to interrupt it, even if the kohen was called. This reservation may be valid even if there is no other kohen present.[10] According to the latter opinions, the kohen is only allowed to duchen if he is up to the same part of Shemoneh Esrei as the chazan at the time of Birkat Kohanim. Under these circumstances, neither walking to the front of the shul nor reciting Birkat Kohanim at its appointed place in Shemoneh Esrei is considered a significant break.
If a kohen may not go up to duchen because he is in the midst of his tefilla, he does not leave the shul. A kohen is instructed to leave shul before Birkat Kohanim either to avoid the obligation to duchen taking effect when he is called upon or as a technical measure, so that people will not think that he is unfit.[11] Neither issue is much of a problem when one is halachically prevented from doing Birkat Kohanim. Thus, neither issue justifies walking out at a time during which one is supposed to be standing in one place.[12]
Let us now discuss strategy regarding finishing Shemomeh Esrei. If you are already up to Elokai Netzor, you can skip or shorten it, as is suggested regarding finishing in order to answer to Kedusha.[13] Since you can answer to Kedusha in that situation,[14] taking part in Birkat Kohanim should be no less important. Even if you do not have enough time to take the three steps backwards, you can still go up at that point. Furthermore, you should remember to take a minimal move toward the duchan during R’tzei and make sure to keep your hands clean since the last time you washed – which, according to most views, can even be the morning washing.[15]
It is obviously not an optimal situation to possibly miss Birkat Kohanim or to have to deal with concerns of timing, which, among other things, is probably disturbing to your concentration. If you feel you can reasonably speed up your tefilla with little to no concentration loss,[16] we suggest doing that. Another possibility discussed by the poskim is to start Shemoneh Esrei somewhat early and thus finish at a workable time. Although it is recommended to start Shemoneh Esrei with everyone else, many permit starting a little early if this results in significant gains.[17] While you are certainly not required to do so, if it facilitates a better frame of mind in your Shemoneh Esrei, you may do so.