My four-year-old uses
Tux Paint all the time. It is fantastic for what he wants. Be sure to
download the extra stamps (6MB) and install. (There are deb/rpm/yum installs.)
If you want a simple program that mimics paint, the kolourpaint mentioned in another post is exactly what you want. I have my system setup to open JPG/GIF/BMP/PNG files with Kolourpaint by default. (I also often right-click and open with Gwenview or GIMP.)
HTH!