Moses isn't mentioned in Chronicles as much as he is in Exodus-Joshua. Naturally. But that doesn't mean that Moses is unimportant to the Chronicler. As James Sparks notes (The Chronicler's Genealogies), Moses is more prominent in Chronicles than in almost every other book outside the Pentateuch.

The Chronicler highlights a specific part of Moses' career: “This esteem is not, however, for Moses’ actions in the exodus. The exodus itself is rarely mentioned in Chronicles, and Moses is only mentioned in connection with it on one occasion. Even then (2 Chr 5:10), Moses is not the one who led the people out of Egypt, he is shown to be the lawgiver, the one who deposited the law tablets into the ark of the covenant. . . . Of the twenty-one times Moses is mentioned in Chronicles, five of the occurrences place him in a genealogy, five as a giver of laws and decrees, two as the builder of the tabernacle, two as commanding a tax for the maintenance of the tabernacle, and seven in relation to the functioning of the cult.”

The Chronicler inserts references to Moses in places where Moses is not mentioned in Kings, and in many of these instances the effect is to highlight's Moses' role as legislator of liturgy. He omits reference to Hezekiah's obedience to Moses, but inserts specifics about what conformity to Mosaic cultic legislation involves: “Hezekiah gathers the priests and Levites and encourages them to purify the temple (2 Chr 29:3–19), followed by sacrifice and burnt offerings by the priests to “atone for all Israel” (cf. 1 Chr 6:34 [6:49]), accompanied by the musicians (2 Chr 29:25–26, 30, cf. 1 Chr 6:16–32 [6:31–47]), with the Levites assisting the priests.” Similarly, the Chronicler does not cite Deuteronomy 6 in his account of Josiah, but instead highlights Josiah's Passover (2 Chronicles 35:2-17). Obedience to Yahweh means obedience to Moses in worship.

The Chronicler's inner-biblical exegesis sometimes replaces the figure of Moses with priests. When the glory of the Lord fills the tabernacle, not even Moses is permitted to enter (Exodus 40:34-35); when the glory fills the temple, it excludes the priests. Moses is included among the Levites, but Aaron and his sons have the higher status of priest.

Moses' authority is prior to that of David. According to Sparks, the cultic changes that David makes are all within the Mosaic framework. David's innovations are not his alone, but are often said to be regulations given by David and someone else - David and Samuel in 2 Chronicles 922 for instance, or David guided by prophets in 2 Chronicles 29:25.

And, more generally, “While the Chronicler presents later kings and leaders as being obedient to the cultic organization of David (2 Chr 8:14–15; 23:18; 29:25; 35:15), he also presents David as being obedient to the cultic commands of Moses (1 Chr 15:2; 16:39–40).”

The Chronicler's use of Moses goes to the heart of his message: “what was vital for the ongoing success of the restored community was the prescribed cultic officials performing the prescribed cultic functions in the prescribed cultic place.” What is most important about Israel's worship is not its beauty but its conformity to God's commandments.