From Physics we know that universe is flat. Also we know that universe have no edges and no center. How can it be that flat shaped object have no edges?

Firstly, see the answer already given on the technical meaning of "flat". Secondly, there is no reason to believe the Universe is finite. There are limits to the amount of it we can see, but there is no indication that it does not continue indefinitely beyond our sight, Or, of course, the opposite. All we can say is that we can see no sign of an edge.

Consider the surface of a sphere. As a two dimensional object it is "flat", in the sense it is not a 3 dimensional object.  It is not "flat" in a three dimensional space. because lines are not restricted to the surface of the sphere.   The "flat" attribute (in normal "context") has no meaning  in a two dimensional space.  You can not measure "flatness" in a two dimensional object.  Just as "straight"  has no meaning in a one dimensional world.  The surface of a sphere has  a non-euclidian geometry.  If you were a point in this surface, you might call this surface "flat", just as our ancestors described the earth centuries before. No wonder they were scared about falling off the edge of the earth. Consider this "surface". It has no center and no edges.  Because it has no edges, every point has the same characteristics of a "center".   Exploring  this "surface" and  comparing it to the universe, is a very interesting game.  If the sphere is expanding away from an "origin" point (its 3 dimensional center), all of the points on the surface appear to be moving away from each other.  We see similar effects in observations of our universe. You see "side path" acceleration:  Nearer objects seem to  be accelerating "away" at a slower rate, and more distant objects seem to be accelerating at a faster rate. The acceleration is real. The  question is: from where is it coming? We look for dark matter and energy to explain this acceleration, because of our desire to hold onto the conservation of energy law.  Another view may be to consider the expansion in an additional dimension.  I know that this idea can and probably already has been refuted, but I find it interesting to consider.  String theory suggests the existence of many additional dimensions. Maybe this "expansion dimension" is just one of those dimensions.  I hear "facts" are claimed to be true, not because they are directly seen, but are asserted because of the measurable side effects.   Maybe an expansion dimension might be considered. Or at best it is just another idea like dark matter/energy.    I am just having fun with these ideas. It's part of my play time. So don't go wasting your time, if you are serious about physics and science. Listen to real professional (teachers) scientists.   I am sure the real scientist will jump all over this. And they are correct. They have much more facts on their side.  If you had some fun thinking outside the box, then that is all I wanted to do. I hope you have a little better insight concerning "centers" and "edges", and related play things.