Complex sentence: From there, he and Fawzi al-Qawuqji left for Baghdad in the Kingdom of Iraq, which was under a degree of British military control, to serve under King Faisal who had been forced out of Syria in 1920.
Split into simpler sentences: From there, he and Fawzi al-Qawuqji left for Baghdad in the Kingdom of Iraq, which at the time was under a degree of British military administration. In Iraq he served under King Faisal, who had previously been forced out of Syria in 1920.