How to fix panel flickering when redrawing?

    Graphics g = drawPanel.CreateGraphics();

Using CreateGraphics() and turning on double-buffering is the worst possible combination. CreateGraphics() gives you a Graphics object that draws directly to the screen. Double-buffering sets up a Graphics object that draws to a bitmap, the buffer used in double-buffering. Then renders the bitmap to the screen at the end of the paint cycle.

So what happens in your code is that you draw the screen directly, something you can barely see but visible if it is slow enough. Then right after that the buffer that you never draw into gets painted. Which wipes out what you drew before. The net effect is heavy flicker with your paint output visible for only a handful of milliseconds.

Using CreateGraphics() was the mistake. You always want to render through the e.Graphics object that you get from the Paint event so you'll render to the buffer. Pass that Graphics object to your drawMonomers() method. Thus:

public void drawMonomers(Graphics g, Point location, string state) {
   // Etc...
}

private void Display1_Paint(object sender, PaintEventArgs e) {
   //...
   drawMonomers(e.Graphics, loc, state);
}

In general, CreateGraphics() has very limited usefulness. You only ever use it when you want to draw to the screen directly and you can afford for whatever you draw to disappear. That is typically only useful in the kind of program that has a render loop that constantly runs, producing new output at a high rate like 20+ frames per second. Like a video game.

Try replacing the Panel with a PictureBox. This worked for me.