After 10 years playing Chad Dimera on the Peacock soap opera “Days of Our Lives,” Billy Flynn is heading to CBS’ “Young and the Restless” in a character not yet revealed. He credits his personal and professional growth during that time to the show that he calls “the little engine that could.”

“We do the best work we can despite the obstacles that we’ve faced as a show. Part of that move I’m excited about is [that] they move slower and there’s more time to do stuff. But I was trained like a warrior here,” he tells Variety with a laugh,...