The Kansas City Chiefs star belted out "Bad Blood" on this week's episode of his "New Heights" podcast ... when he and his big bro, Jason, were talking about the Eagles' recent addition of Kenny Pickett.

Jason told the audience his former team acquired the quarterback in a trade with the Steelers ... before Travis jumped in to explain Pittsburgh simply had to make the move because the former first-round pick was upset over the recent addition of Russell Wilson.

"Kenny and the Steelers," he said, "their relationship ended in a little baaaaaaad bloooood!"

"Because," Travis continued, "Kenny is saying he preferred to move on."

Jason let the tune go without further reaction -- and the two didn't make reference to Travis' girlfriend again during the episode.

Travis, though, did talk about a night out in L.A. that he had sans Swift last week -- raving to Jason about the Justin Timberlake show he attended.

Travis gushed about the "Suit & Tie" singer's concert -- calling it a "fun evening" while urging all of his fans to buy JT's new album.