Typically, monarchs wear gleaming crowns atop their heads for one reason – because crowns are a visual symbol of power. In King Lear, Shakespeare often associates crowns with a loss of power and the king's deteriorating mindset. Let's think about this for a moment.
At the beginning of the play, Lear's Fool makes an interesting joke about the king's "crown" after Lear decides to give his kingdom to his evil daughters: "When thou clovest thy / crown i' the middle and gavest away both parts, thou […] hadst little wit in / bald crown […]" (1.4.14). In other words, the Fool implies that once Lear divided ("clovest") his power (which was like cutting his "crown" down the middle into two parts) among his two daughters, he exercised poor judgment in his head ("bald crown"). Of course, the Fool is playing on the dual meaning of "crown" (a head or, the thing a king wears on top of his head) in order to demonstrate that Lear's decision to give up his crown and divide his power reflects an unstable mind.
The idea that there's a relationship between Lear's crown, his lack of power, and his state of mind shows up again later in the play. In Act 4, Scene 6, Lear enters the stage wearing a "crown" of wildflowers atop his head instead of a proper crown made of precious metals and gems. Here, Shakespeare emphasizes Lear's complete and utter loss of power, as Lear has long since divided up his kingdom among his daughters and has been stripped of all his authority. The "crown" of wildflowers also signifies Lear's deteriorated mental state and complete descent into madness – the idea being that what Lear wears on top of his head (wildflowers) is an accurate indication of what's going on inside Lear's head.