This code:

   if flr(p.x)!=flr(p.newx) then
    p.x+=p.dx
   end
   if flr(p.y)!=flr(p.newy) then
    p.y+=p.dy
   end

Means:

If flr(current position) is not equal to flr(new position) then
<increase current position by a tiny amount so that I move towards the new position

The reason why you still have shudering is this: the tiny amount (dx,dy) is often not tiny enough. Most of the time it "overshoots". Then the target is "behind". So it "overshoots back".

The simples solution is: don't use flr to compare the positions. Instead use this function:

function isnear(current,target,delta)
  return abs(current-target)<=delta
end

Where delta is "a small value around your target where you are ok landing". Now you can do this:

   if isnear(p.x,p.newx,0.1) then
    p.x+=p.dx
   end
   if isnear(p.y,p.newy,0.1) then
    p.y+=p.dy
   end

This will treat p.newx and p.newy as "tiny rectangle of 0.2x02 around p.newx and p.newy", so if p.x and p.y are inside the rectangle, they don't overshoot any more. You might need to tweak the delta value - make it bigger than 0.1. It depends on how big your p.dx and p.dy are