Aside from the silly superstitions (just because three people share the same name doesn’t means we can draw prophecies on how their lives or work–or reign–will pan out):

– Yes, Charles I was beheaded.  A number of historical factors are the cause but it is broadly true that he was a remarkably unpopular king who fought to extend his royal prerogative towards absolutism, fought with parliament, levied taxes without the consent of parliament.  Charles III does not the have the options to follow any similar path, there is a much more systematised constitution in place in the 370 years since then;

– Charles II cannot be described as having a reign that « did not go well ».  Rather, it was remarkably successful: he sponsored the Arts and Sciences in a way that led to England (and Britain’s) later leadership in these fields, founded the Royal Society, helped reduce the seriously negative impact of puritanism, personally directed the firefighting efforts during the Great Fire of London 1666.  Yes he had a number of children by mistresses but in the context of the 17th Century has absolutely nothing to do with the quality of his reign.

– Charles III is living 3+ centuries later in SIGNIFICANTLY different times. Over the centuries governance has been remarkably transformed by the Glorious Revolution (1688), the handing over government from kings to ministers responsible to parliament, the subsumption of royal prerogative by ministers, the codification of law-making by parliament, etc. 

Difficult to see how you draw these links between these three men who happen to share a name.  Or, when William V is on the throne, will we ‘prophesy’ his reign on the basis that his namesake William IV also had c. 10 illegitimate children by mistresses, or that William II died after being accidentally shot with an arrow by one of his own men?