There is the clone tool. It has a couple of settings and 2 modes for reference spot selections. It works in the same way as the clone tools in other editors.
The burn and dodge functionality is more or less covered by the retouch tool. You can choose the sub-more in its configuration panel. RWPaint uses neutral rather than photographic terminology and so Brighten is similar to dodge while Darken is similar to burn. Alternative way to achieve these effects would be via Multiply color and 'Add color'' modes there, but these depend on current color.