Our practice follows the custom of the Arizal to remain sitting during Kaddish. Although Ashkenazim make a point of standing for Kaddish, Sephardic practice is to remain seated.
The exception to this rule is the Kaddish recited before Barechu at the beginning of Arbit on Friday night, when many have the custom to stand. The Arizal taught that one should stand during this recitation of Barechu, as part of the extra Shabbat soul descends upon a person at this point. Therefore, since in any event one stands for Barechu, many have the custom to stand already during the Kaddish that precedes Barechu. As a general rule, however, Sephardic custom allows one to remain sitting for Kaddish.
This applies only if a person was sitting before Kaddish began. If one was already standing when Kaddish starts, then he must remain standing. This was the practice of the Arizal.
According to some Poskim, if one was standing when Kaddish began, then he must remain standing throughout the entire recitation of Kaddish. Others maintain that one must remain standing only until the Hazzan reaches "Da'amiran Be'alma Ve'imru Amen." Our custom follows a third opinion, that of the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) – that one may sit after he completes his "Yeheh Shemeh Rabba" response, which, according to our community's practice, ends with the words "Da'amiran Be'alma." Once a person completes his response, he may sit, even though the Hazzan has not yet reached "Da'amiran Be'alma." Some have the misconception that it is improper to sit before the Hazzan reaches "Da'amiran Be'alma," but in truth, one may sit once he reaches that point.
On Friday night, the congregation stands during the recitation of Vayechulu and the Hazzan's recitation of "Me'en Sheba," which is then followed by Kaddish. In some synagogues, people rush to sit down after the Hazzan concludes "Me'en Sheba" (with the recitation of "Baruch Ata Hashem Mekadesh Ha'Shabbat"), before he begins Kaddish, so they would not have to remain standing during Kaddish. Some Hazzanim even pause before Kaddish to give the congregants the opportunity to sit before Kaddish. Hacham Ovadia Yosef writes that this is improper, as specifically rushing to sit down before Kaddish begins shows disrespect to Kaddish. He brings as an example a ruling of the Ma'amar Mordechai (Rav Mordechai Karmi, 1749-1825) regarding the situation of somebody standing next to a person who is about to begin the Amida. Halacha requires one to stand if the individual next to him is reciting the Amida, unless he was sitting before his neighbor began the Amida, in which case he may remain seated. The Ma'amar Mordechai writes that one who is standing and sees that the person next to him will soon begin the Amida should not rush to sit down so he would not need to remain standing. By the same token, Hacham Ovadia writes, it is inappropriate to specifically rush to sit down before Kaddish in order to avoid having to stand during Kaddish.
During Arbit, one may remain seated during the recitation of the Kaddish that precedes the Amida. Since one is already seated during Hashkibenu, he may remain seated for Kaddish, and then stand for the Amida prayer.
On days when Tahanunim are not recited after the Hazzan's repetition of the Amida, and only the brief "Yehi Shem" recitation precedes Kaddish, it is proper to remain standing for Kaddish.
Some people mistakenly think that they may sit down for Kaddish – even though they had been standing before Kaddish began – if the Hazzan sings the Kaddish and thus prolongs its recitation. This is incorrect; one must remain standing even if the Hazzan sings the Kaddish. However, the Poskim write that if the Hazzan knows that people are standing, he should ensure not to prolong the recitation of Kaddish, in order not to overburden the congregation by making them remain standing for several minutes.
This Halacha alerts us to the care that must be taken to avoid "Tirha De'sibura" – causing the congregation even minor inconvenience. If Hazzanim are discouraged from prolonging the Kaddish recitation by several minutes when people are standing, then this shows us the sensitivity that Halacha requires toward the congregation. In fact, a well-known Hazzan told me that when he led the service on the High Holidays in Hacham Ovadia Yosef's synagogue, and he wanted to sing a special melody for Birkat Kohanim that was traditionally sung in Jerusalem communities, Hacham Ovadia instructed him not to. He explained that it would be inconsiderate to overburden the congregation who are standing during Birkat Kohanim – especially on Yom Kippur, when the people are fasting – by prolonging this part of the service. Unfortunately, it has become common to sing a great deal at Huppa ceremonies, which causes a great deal of inconvenience to the guests, and this practice should be discouraged.
Summary: Sephardic custom is to remain seated during Kaddish. If one was standing before Kaddish began, then he must remain standing until he completes his "Yeheh Shemeh Rabba" response, through "Da'amiran Be'alma," at which point he may sit, even if the Hazzan has not yet reached "Da'amiran Be'alma." A Hazzan who knows that people are standing for Kaddish should not prolong the Kaddish recitation. It is improper to rush to sit down before Kaddish to avoid having to remain standing.