There are various Sephardic customs for how to arrange the arba minim. The Ben Ish Chai's halakhic works and responsa never explicitly refer to what he did. Nevertheless, the most common custom today among Sephardim is follow the Arizal, who was a primary influence on the Ben Ish Chai and many Sephardic authorities generally.
The custom of the Arizal is referenced in Magen Avraham (651:4):
הטעם ע"פ הקבל' [ד"מ מהרי"ו] עיין בלבוש ובכתבי האר"י כת' לאגוד ג' הדסים א' בימין הלולב וא' בשמאל וא' באמצע וב' ערבות א' בימין וא' בשמאל ושל"ה כת' בשם מט"מ ערבה בשמאל והדס בימין ולולב באמצע
The custom to raise the hadassim higher is according to our master R. Yaakov Weil. Also see the Levush and the writings of the Arizal, which state that one must bind the three hadassim so that one is to the right of the lulav, one to the left, and one in the middle. For the two aravot, one is to the right [of the lulav] and one to the left. The Shelah writes in the name of the Mateh Moshe that the aravah is to the left and the hadassah is to the right and the lulav is in the middle.
Ashkenazim generally follow the latter approach, where the hadassim are to the right and the aravot is to the left (Mishnah Berurah 651:12).
The Yalkut Yosef (651:10) follows the Magen Avraham in declaring it the Sephardic custom:
יתן ההדסים אחד מימין ואחד משמאל, ואחד באמצע על גבי השדרה, ונוטה יותר לצד ימין, והערבות אחת מכאן ואחת מכאן, ויקשור
One hadas is to the right and one to the left and one in the middle on the spine [of the lulav], and one aravah here and one there [left and right], and you bind them.
As noted, placing the hadassim at a higher level than the aravot is also a popular custom, particularly among Ashkenazim. The Rema (651:1) brings down R. Weil as the source (and Magen Avraham is commenting from there), and this is also a common custom among Sephardim.