I think Nick Adams would be a wonderful choice as Billy Flynn. He has extensive experience with theatre..including Chicago. He can sing, act and dance.....an amazing triple threat. Another possibility would be Cheyenne Jackson. As the late Judy Tenuta used to say: "It could happen"!
"Noel [Coward] and I were in Paris once. Adjoining rooms, of course. One night, I felt mischievous, so I knocked on Noel's door, and he asked, 'Who is it?' I lowered my voice and said 'Hotel detective. Have you got a gentleman in your room?' He answered, 'Just a minute, I'll ask him.'" (Beatrice Lillie)