What color makes you look thinner depends on various factors which are inextricably related. These include the camouflage quality of the chosen color, the tone or shade of color, and the quality of the cut of the clothes and how that impacts on your shape. It also includes the suitability of the color for the given occasion. A color which jars will make you and your figure noticeable when a more suitable one will not.
It would be easy to say black is the color which makes you look thin because it hides shape, seems to mask size, goes with anything and can look good. But it's a non color and the color of shade. A world with everyone dressed only in black is a depressing thought and black doesn't look good on everyone.
The first point to consider is what color flatters your complexion. Which are the tones, shades and combinations of that color which give your appearance a lift? The colors you wear should emphasize your good points, drawing attention away from the bits of you you don't want noticed. People will be less likely to notice your outline if what you wear makes you look healthy and confident. This is why advice is given to draw attention to your face, away from your body. This is where you can experiment to find out which color is best. Scarves are an inexpensive way to experiment with a variety of colors. You can drape them round your neck and shoulders to see which you feel gives the most flattering result. When you find colors you like, try larger pieces of material to see what the overall effect has. Then, before you buy anything, you know exactly what you are looking for.
Some people look wonderful in various shades of green, others are drained of natural color and look ill. Blue eyed blonds, generally, can wear shades of blue which enhance their eyes, again taking the eye of the viewer away from the figure.
A tanned, or brown skin, is set off with white or shades of cream. Yellow, like green can be a tricky color, but if you find the right shade, and it's one of your colors, it can be beautiful. Pink can give color to pale skins, and it can help aging skins. Terra cotta has so many tones it can flatter a variety of skin tones.
Having a coordinated color scheme can also make the best use of your chosen color. If your clothes are well put together with shapes that suit your body, the outfit will appear more glamorous and you will appear thinner, or at least observers will not notice size because you look good.