This Luth-AR .223 Bull Rifle Kit should not be used with 5.56. A barrel chambered in 5.56 can safely use both .223 and 5.56. The same applies for barrels in .223 Wylde. You can find out more from this how-to guide that explains the differences between 5.56 and .223:
https://www.opticsplanet.com/howto/223-remington-vs-5-56mm-nato-ammo.html