For consistency and to make users recognize quickly clickable links/buttons, "the color of a button should depend on its state and its purpose"*.
In the case of the hamburguer button it does not behave as a link but it needs to call to action as links do.
Based on this I would think that it makes more sense to display it with the same color as the links, but in general I see this button in a different color than links, (more like in the text color) e.g.:
So what is the right path to follow?