If a person hears Kaddish or Kedusha while he is reciting the Amida prayer, he may not interrupt his recitation to answer to the Kaddish or Kedusha. Instead, he should remain silent and listen to the Kaddish or Kedusha, without answering.
Does this apply in a case where a person hears Kaddish or Kedusha immediately after he has recited the introductory verse to the Amida, "Hashem Sefatai Tiftah U’fi Yagid Tehilatecha"? This verse is not actually part of the Amida; its recitation was instituted later as an introduction the prayer, but not as an actual part of the Amida. Seemingly, then, it should be permissible to answer to Kaddish or Kedusha after reciting "Hashem Sefatai," so long as one has yet to begin the actual Amida with the words "Baruch Ata."
The Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) addresses this issue in Parashat Vayakhel, and rules that the Halacha in such a case depends on which prayer is being recited. If this occurred when one has begun reciting Minha or Musaf, then he may, indeed, respond to the Kaddish or Kedusha, because, as mentioned, he has yet to begin the Amida prayer. After the Kaddish or Kedusha, he should then repeat "Hashem Sefatai Tiftah" so he can introduce his Amida prayer.
However, in a case of one praying Shaharit or Arbit, he may not interrupt to answer to Kaddish or Kedusha, despite the fact that he has not yet begun the actual Amida. At Shaharit and Arbit, Halacha requires "Semichat Ge’ula Li’tfila," which means that one begin the Amida immediately after concluding the previous Beracha of "Ga’al Yisrael," without interruption. Therefore, even though one has not begun his Amida by reciting "Hashem Sefatai Tiftah," it is nevertheless forbidden for him to respond to Kaddish or Kedusha at this point because he will then be interrupting in between the Beracha of "Ga’al Yisrael" and the Amida. In this case, he should pause, listen silently to the Kaddish or Kedusha, and then begin his Amida with "Baruch Ata Hashem…"
It must be emphasized that once a person began the actual Amida text by reciting "Baruch Ata," he may not interrupt for Kaddish and Kedusha, even at Minha or Musaf, since he is already in the middle of the Amida.
Summary: One who hears Kaddish or Kedusha while reciting the Amida listens silently, without responding. If he hears Kaddish and Kedusha after he recited the introductory verse of "Hashem Sefatai Tiftah" but before he has begun the Amida, he may answer to Kaddish or Kedusha if this occurred during Minha or Musaf. If this happened during Shaharit or Arbit, then he may not answer to Kaddish or Kedusha, since no interruptions are allowed in between the Beracha of "Ga’al Yisrael" and the Amida.
