He compares the data of Solomon's reign as it is described in 1 Kings with other ANE monarchs. Whereas Solomon receives tributes of 120 shekels of gold, other kings (notably Rameses III) received much more. Even his 666 shekels of gold in taxes every year isn't that impressive compared to Mari and Egypt. Similarly, Solomon only has one golden and ivory throne. The Egyptians would give 10 at a time as gifts to the Aramians and Hittites.
Kitchen's point is that in reading about Solomon, we are not reading about King Arthur. As a believer in the reliability of Scripture, I would never disbelieve 1 Kings even if it said more spectacular things about the early United Monarchy. Nevertheless, even if we look at the narrative without a high view of Scripture, what it says about the United Monarchy is totally plausible by the standards of the times.