The Ben Ish Hai (Rabbi Yosef Haim of Baghdad, 1833-1909), in Parashat Vayigash (Halacha 3; listen to audio recording for precise citation), raises the question of whether one may answer "Amen" during the Pesukeh De’zimra section of the prayer service, after Baruch She’amar. He writes that if one hears a Beracha during Pesukeh De’zimra, then he answers "Amen" to the Beracha. Thus, for example, if after a person recites Baruch She’amar he hears somebody next to him recite the Beracha over the Tallit or Tefillin, he answers "Amen" to that Beracha. The Ben Ish Hai makes reference to the testimony of Rav Haim Vital (1543-1620) that the Arizal (Rav Yishak Luria, 1534-1572) would answer "Amen" to Berachot during Pesukeh De’zimra, and this is the correct practice to follow.
It should be noted that one does not answer "Baruch Hu U’baruch Shemo" if he hears a Beracha during Pesukeh De’zimra; although he answers "Amen," he should not answer "Baruch Hu U’baruch Shemo."
What is less clear, however, is whether one may also interrupt Pesukeh De’zimra to answer "Amen" to the final responses of the Kaddish recitation. One certainly answers "Amen" to the first five responses of Kaddish, through "Da’amiran Be’alma." The Ben Ish Hai was unsure, however, whether one also answers "Amen" to the later responses of Kaddish. He therefore advised that one should not answer "Amen" to these responses, as otherwise he runs the risk of making an unwarranted interruption in Pesukeh De’zimra.
Summary: One who hears a Beracha while he recites Pesukeh De’zimra should not answer "Baruch Hu U’baruch Shemo," but does answer "Amen." If one hears Kaddish while he recites Pesukeh De’zimra, he answers "Amen" to the first five responses – through "Da’amiran Be’alma" – but not the subsequent responses.
