If a person hears Kadish, Barechu, Kedusha or a Beracha as he recites Baruch She’amar, should he interrupt his recitation to respond?
The Ben Ish Hai addresses this question in Parashat Vayigash (Halacha 9; listen to audio recording for precise citation), and he distinguishes between the two sections of Baruch She’amar. Before one has reached the Beracha in Baruch She’amar ("Baruch Ata Hashem Elokenu…Ha’Kel Ha’ab…"), he may answer "Amen" to all Berachot, and to Kadish, Kedusha and Barechu. However, in such a case one should preferably then return to the beginning of Baruch She’amar, so that he recites it in its entirety without any interruption.
If one has already begun reciting the Beracha in Baruch She’amar, the Ben Ish Hai rules, then he may not answer "Amen" to any Berachot. He may, however, answer to Barechu, and if he hears Kedusha, he may answer "Kadosh Kadosh" and "Baruch Kebod." He does not recite the verse of "Yimloch." As for Kadish, the Ben Ish Hai rules that one may interrupt the Beracha of Baruch She’amar to answer the first five "Amen" responses of Kadish, through "Da’amiran Be’alma." (The Shulhan Aruch maintains that one responds only until the word "Yitbarach," but we follow the practice of the Kabbalists to continue until the word "Be’alma.") Furthermore, if one hears the Hazzan reach "Modim" in the repetition of the Amida while he recites Baruch She’amar, he should recite the three words of "Modim Anahnu Lach" together with the congregation.
Summary: One who is reciting the first section of Baruch She’amar (before "Baruch Ata Hashem Elokenu…") may answer "Amen" to all Berachot and respond to Kadish, Barechu and Kedusha. In the second section of Baruch She’amar, one interrupts only for the first five "Amen" responses of Kadish (until "Be’alma"), Barechu, the verses of "Kadosh" and "Baruch Kebod" in Kedusha, and the first three words of Modim De’rabbanan ("Modim Anahnu Lach").
