If her record gets wiped, which is a possibility, her rank would, in theory, be restored as Commander. That much is plausible within the context of Discovery. Her gaining a captaincy would take a lot longer since she would not only have to earn the trust of her commanding officer to recommend her for such a position, but she would also have to get over the stigma of her expunged record to the Admiralty. Should she remain in Starfleet following the war (as oppose to returning to her life sentence, which I would gather will be removed for her actions during the war, or are permanently suspended due to Captain Lorca's efforts to get her on his ship and under his command, even as a Specialist, than she would likely climb up the ranks again.
She might not be captain within the next two decades, but if she's still in Starfleet and her record is expunged, eventually those old Admirals will retire or the cloud over her will fade (for most people....there will always be someone who blames her for the war and their lost kin). At which point, assuming she does actually have command qualities as Captain Georgiou suggests, will be promoted to captain of a starship. Because, if that is her best destiny, anything else would be a waste of material, as her brother says to one Admiral Kirk.
She is a little bit older than James T. Kirk. He however went up the ranks quickly. Burnham, if there was no war, might have gotten her first command after being in Starfleet for say eight years, depending on how quickly Captain Georgiou was intending for Michael to get her own ship, or if she was laying the foundation of the idea in Michael's head so she would excel in that direction and get her own command within the next three years or so. Kirk (in this universe at least) became captain in less than ten years from graduating from the Academy. It is possible he was in command of a ship prior to getting USS Enterprise from Pike. We don't know for sure. But with Burnham's record hanging over her head (even if it is expunged) her career will do a restart, and it will take time to become a captain. If she does make it, she would probably still be a captain of a starship during the time Kirk was an Admiral. She would probably never make admiral, but that might suit her just fine. Retire by the beginning of the 24th century if she lives that long and reaches the 75 year retirement age around the time Picard is born.
And I have heard people suggest that Michael Burnham could be retconned into being the Captain of USS Saratoga in 2286 (as played by Madge Sinclair). Burham would be around 60 years old at that time.