Normally, I believe one would render 1 Chronicles 29:20 (LXX) as the NET Bible does:
"David told the entire assembly: 'Praise the Lord your God!' So the entire assembly praised the Lord God of their ancestors; they bowed down and stretched out flat on the ground before the Lord and the king."
KURIWi and TWi BASILEI (grammatically) should both receive the action delineated by the verb PROSEKUNHSAN. While I could not find another example that described two entities receiving worship as direct objects by the use of a datival construction, I believe that Rev. 14:9-11, with its mention of the beast and its image, well illustrates how 1 Chron. 29:20 should be understood. Notice that PROSKUNEI + the accusative is used in Revelation 14:9, 11. But both objects receive the action of the verb. This also seems to be the case in 1 Chronicles 29:20 and translators usually recognize this point. Theology seems to have influenced Brenton's LXX translation. He renders the verse: "And David said to the whole congregation, Bless ye the Lord our God. And all the congregation blessed the Lord God of their fathers, and they bowed the knee and worshipped the Lord, and did obeisance to the king."
Thomson's LXX states:
"Then David said to all the congregation, Bless ye the Lord our God. And all the congregation blessed the Lord the God of their fathers, and with bended knees made a reverence to the Lord and to the king."
I find it interesting that the Vulgate also explicitly shows that both God and the King receive the same action. It says:
benedixit omnis ecclesia Domino Deo patrum suorum et
inclinaverunt se et adoraverunt Deum et deinde regem.
"they worshiped [or adored] God and then the King."
The NETS LXX similarly renders the latter part of 1 Chron. 29:20,
"and did obeisance to the Lord and the king"