I concur with Durbanville and Lit24 on the definitions of 'Flat' and 'Static' characters versus the 'Round' and 'Dynamic' characters in literature. In summary, a Flat or Static character in a story remains unchanged. On the other hand, a Round or Dynamic character changes within the story.
In a “Midsummer Night’s Dream” by William Shakespeare, there are a number of characters that exhibit the Dynamic and Round aspects and they include Demetrius, Lysander and Puck. In the beginning, Lysander loves Hermia but Hermia’s father Egeus, wants her daughter to marry Demetrius. After Puck's enchantments Lysander pursues Helena, then later near the end he reverts back to loving Hermia. Demetrius faces a similar situation where, due to Puck's enchantments, he stops pursuing Hermia and instead goes after Helena. Puck works for Oberon’s selfish interests but at the end seeks forgiveness.
Some of the characters that remain flat include Egeus and the fairies working with Bottom. Egeus wants his daughter to marry Demetrius even after the situation changes. The fairies run away from Bottom after he is enchanted with an Ass’s head, but when the situation resolves they just go back to their routine.
In A Midsummer Night's Dream there is certainly a range of round, dynamic characters who stand out from the flat, static characters because in literature, it is necessary to use different types of characters who serve different purposes and therefore audiences and readers come across the well-rounded characters to whom they can easily relate, those who are complex and have character traits which define them and which often cause conflicting emotions within those characters. These are usually the dynamic characters and the audience watches those characters develop over time and often change their stance.
In contrast, flat characters are almost one-dimensional and uncomplicated and display only a few character traits which remain consistent but from which the audience or reader cannot really gain an understanding of the character. These are usually the static characters who have no bearing on the advances within the story and do not change because of them. Unlike dynamic characters, they do not experience personal growth before or after the events of the play or story.
In the play, the audience learns a lot about Hermia. She is a determined character and must find a way to defy her father's demands that she marry Demetrius when she loves Lysander. If she does not marry Demetrius, her father intends to send her to a nunnery. Hermia does not intend to "yield my virgin patent up" (I.i.80) meaning that she will not marry Demetrius and so, taking matters into their own hands, Hermia and Lysander run away into the forest. She will be one of the more rounded and certainly dynamic characters in the play as she has to develop and change and adapt to her shifting circumstances.
The most obvious flat and static characters would be Bottom and his crew who serve an important purpose in relieving the tension within the play but who do not contribute to the outcomes. Their characters do not change throughout.