So when people breathe heavily their chest fills with oxygen, not their stomachs. I made a rough edit giving him that effect. I only really used 3 colors for the animation of the chest even though you kind of had colors all over the place. Animation efficiency relies on less colors and a smaller canvas. If you are going for detail or a certain style then by all means use as many colors as you like but just know that the pay off is that your sprites will take a lot longer to make and if you are planning on using them in a game or whatever you will have to allow yourself a lot more time to make said game.

Anyway here he is:

It's not perfect by any means but I am trying to illustrate that movement can be represented in different ways. You'll notice at his stomach that his outlined shape does not change at all but you can hopefully see that he is pulling his diaphragm in while his chest expands. This is done simply by using the dark and light colors to represent depth and using darker colors for concave and light colors for convex surfaces. This is pretty common in art as your eyes will automatically push darker, less saturated colors to the background and lighter more vibrant colors to the foreground.

The other thing you will notice is that his chest grows a lot to the point where it's almost ridiculous. This expanded chest is extreme and might not be what you are going for but sometimes it is necessary at such a low resolution as there isn't much wiggle room for movement as it's either moving one pixel or moving no pixels.

I would suggest giving it another go with this new information and seeing what you can do with it. I would also suggest trying to make as much as you can move around on each new frame, like if you move an arm, you should move his shoulder, move his chest and in turn move his whole body. When people move one part of their body, the rest of their body is never static.