Moore, 26, is a former third-round pick of the Raiders back in 2013. Moore spent two seasons in Oakland before being traded to the Colts in return for a 2016 sixth-round pick.
Moore was in the final year of a four-year, $3.054 million contract when he was released by the Colts a few months ago. The Chiefs signed him to a contract soon after but they elected to waive him earlier in the week.
This year, Moore has appeared in five games and recorded 30 tackles for the Colts. according to Pro Football Focus, Moore is rated as the No.74 linebacker out of 87 players.
Barrington, 26, is a former seventh-round pick of the Packers in 2013. He is in the final year of his four-year, $2.209 million contract with a base salary of $675,000 for 2016.
Barrington was waived by the Packers coming out of preseason, but was later claimed off waivers by the Chiefs. Kansas City cut him loose earlier in the week.
In 2016, Barrington has been active for two games but has yet to record any statistics.