Richard Burton's performance of Henry VIII certainly cannot be described as a subtle screen performance. Instead it is an extremely hammy performance that can easily be described as a very over the top creation, and characterization of the King. Burton never suggests many hidden emotions of Henry very much instead he constantly puts the emotions of Henry out to the forefront.
Burton's performance is hammy, but this does not really mean that it is exactly bad at all. Bad and over the topness do not exactly go together it is if it compromises the idea of effective characterization when it does. Burton here does go hammy constantly but in the role of the boisterous larger than life King Henry VIII this is sort of the right approach for Henry. Burton certainly is capable of subtle performances, such as in the Spy Who Came Who Came in From the Cold, so I really think this was very much purposeful over acting, certainly not do to incompetence is what I am saying. As Henry he most certainly yells a lot gets red and viscous looking when angry, smiling devilishly when happy, everything is telegraphed most certainly, which does fit Henry actually since he was a King, or at least as portrayed here, who made it known what he wanted.
Also there are a few moments that are nicely handled when he attempts to be a little less obvious in his performance such as suggesting that he does love Anne for example. These are not exactly the reactions of say Robert Duvall in Tender Mercies, but he has a few good smaller reactions now and again. Does Burton overdo it from time to time, well most certainly, but I never think it becomes out of character obvious acting though. Even the most extreme obvious emotional scenes are of Henry's character. Henry is always pushing his emotions in everyone's faces as Burton portrays him, and by that he cannot be ignored as Henry really should be.
Now I think I praised this performance enough, because still on the whole it could have been better than it is. I think he could have reigned in his performance just a little when he did go over the top it could have been more effective. Also I think he frankly could have been a tad more charming as Henry as he is since his Henry is extremely unsympathetic more than he really needed to be. A much better example of a flamboyant performance can be found in Becket with Peter O'Toole's turn as Henry II, which is a perfect example of what this performance could have been. Burton really could have been far more entertaining, far more effective, and far more interesting than he is if he just played Henry with a little more ease, it still could have been hammy sure, but just a little less ham or at least some better used ham would have been a good idea.