The first thing to avoid is resizing in the draw() method this is bound to cause flickering. Also we only want to resize if the frame has actually been resized. Since Java does not provide a resize event then we need somewhere else to check for resizing. We can do this in the pre() method this method is called just before the draw() method every loop.

I can't think of a way to get rid of the flickering entirely but although not perfect this works reasonably well.
Code:

int canvasHeight = 500;
int canvasWidth = 500;

void setup(){
  size(canvasWidth,canvasHeight);
  frame.setResizable(true);
  background(300);
  registerPre(this);
}

void pre(){
  if(width != canvasWidth || frame.getHeight() != canvasHeight){
    resizeWin();
  }
}

void draw(){
  rect(30, 20, width - 60, height - 40);
}

void resizeWin(){
  canvasHeight = frame.getHeight();
  canvasWidth = frame.getWidth();
  setPreferredSize(new Dimension(canvasWidth, canvasHeight));
 }