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Yes, he used barrier haki on Kaido in chapter 1026 against dragon kaido. He learned both barrier and internal destrcution from hyougoro in udon. He also used barrier haki+ internal destruciton haki on his newer version of king kogn gun in chapter 955.

For the no touching technique, you need Advanced armament Haki Barrier and CoC Caoting together. The reason Luffy's attacks are so devastaing is because he used Adv CoC and Barrier + internal Destruction to injure kaido signicantly.

Big mom does not have internal destruction haki, it is the same reason Yamato also could not take off her cuffs. She had no internal destruction haki. That haki is very rare. Only Garp, Luffy, Shanks, Roger and Rayleigh have it.