You do not need "flashy" tools. You can do flat design even in Microsoft Paint, which is the simplest program ever.
You can simply use the Path tool to make a shape, convert it to a selection and fill it with a color or gradient. Here's a tutorial.
But in reality using GIMP is the wrong approach. You should use a vector based program, such as Inkscape.
These kinds of images are based on simple geometric shapes, so just pay attention to what you want to do. Imagine a Sesame Street program. "Where do I find a triangle? Let's go find me a triangle".