Just had a quick look and I think I know how the rumour started. There is an Empire article with the headline "Dexter Fletcher Will Direct Sherlock Holmes 3 With Robert Downey Jr" that could make people think they are directing it between them.
I remember watching Fletcher in Press Gang when I was a kid. Was your usual kids fare kind of drama with him and Julia Sawalha about a school newspaper, but there was one stand out episode that I can still remember one scene from even now where he is trapped after an explosion in a shopping centre trying to get to someone he can hear crying for help only to find that he's hearing her voice through a broken pipe and she is on another floor.
He's underrated and very talented as an actor and given the response to Rocketman I'd say he has his director's chops as well. 
just got to get to 2021 then
