First, Eustass Kid has tangled with 3 of the Yonkos with no fear.


 

He lost his left arm to just above the elbow during the two year timeskip in a battle against the Red Hair Pirates.


 

Then he proceeded on sink Big Mom’s ships as well as try to invade her island.

Kid encountered Kaido when the latter fell out of the sky and landed at the Kid Pirates’ hideout before coming face to face with the rookie pirate. Scratchmen Apoo and Basil Hawkins joined Kaido out of fear while Kid refused to do so.


Came back after escaping from prison just to save his Nakama.

 

He is very similar to Luffy in his fearlessness and will never be a subordinate of anyone. He also possesses Conqueror’s Haki just like Luffy.


I think these are the reasons why Luffy respects him too.