However, after just six ineffective outings he was traded to the St. Louis Browns for pitcher Sam Zoldak, missing out an opportunity to play in the World Series, which the Indians won.

In March 1952, Kennedy was purchased by the Chicago White Sox, ending his four-year tenure with the Browns at a 12–24 record with a 4.84 ERA.

Despite his success in Chicago, that winter he was packaged with pitcher Marv Grissom in a trade to the Boston Red Sox for shortstop Vern Stephens.

Alas, the trade failed to work out for either side; Stephens and Grissom were both dealt again by mid-season, and Kennedy was demoted to the minors, where he stayed for the remainder of the 1953 season and all of 1954 and '55.

In eight major league seasons, he had a 15–28 win–loss record, 172 games pitched (45 starts), 11 saves, 256 strikeouts and a 4.73 earned run average (ERA).