The characters in A Midsummer Night’s Dream are flat characters as opposed to round characters because none of them are fully developed.

A flat character is just that—one dimensional.  The character has a few character traits that are clearly defined, but there is little depth to the character and the character will not change.  A round character, on the other hand, is multifaceted and strongly developed.

We do not spend much time with any of the characters in this play.  Most of them can be defined as wanting to be with this person or that person, or wanting this.  Hermia wants to marry Lysander.  Oberon wants Titania’s changeling.  Egeus wants Hermia to marry Demetrius.  Puck wants to create mischief.  There are no deeper motives for what they are doing.

Consider Hermia, a character that might have been round. She is kind of interesting.  Unlike most of the women in Athens, she stands up for herself.

I do entreat your Grace to pardon me.(60)
I know not by what power I am made bold (Act 1, Scene 1)

Hermia says she does not know where she gets the guts to refuse to marry Demetrius, or to ask what will happen to her.  Yet we don’t know where she got the guts.  We never get to experience much more from Hermia.  She runs off with Lysander to marry him, and then she chases him through the woods and fights with Helena.  They want what they want, and there is nothing more to it than that.  There is no hidden motivation, no growth, and no depth.