What type of map did you pick? Go for diffuse, and untick the shadow and lighting options at the bottom. I haven´t really tried it out, but it should work allright if i´m not mistaken.
Thanks for the reply StJoris. I tried bake to texture with padding set to 1 and diffuse map but the problem just got worse. And the lighting gave the texture more shadows. (The original was self illuminated) I guess I'm doing it wrong somewhere?
how does your uv overlays that texture, could you show us that? And if you want to bake without adding new shadows to your diffuse, you have to select the material for your object and then set it to 100% self illuminated. I'd just try to paint the border, cus you only have one colour, so just paint it black.