Kung Fu Fighting is a guilty pleasure of mine - I do love this song!
"Funky" has changed in meaning over the years. Back in the 1970s, when this song was originally recorded, "funky" meant cool or hip, current and trendy. Today, however, "funky" has two different meanings. It can describe something that is unusual, but still "cool." It can also describe something that has spoiled or something that smells bad: "Please have this mint, your breath is really funky!"
Billy Chin and Sammy Chong are just made-up names for characters in the song.
"Big Boss" can have several different meanings; in general usage it refers to the person in charge. In the song, they're referrring to the leader of a rival gang. "Get it on" in this case means "let's start the fighting." ("Get it on" is common usage, but its meaning changes depending upon the context. For one thing, it can mean "let's have sex.")
"Make a stand" is common usage; it means to hold firm against something or someone.
"Made him skip" in this sense means he was momentarily startled. "We're into a brand new trip" means the entire situation has suddenly changed.