I know that red light travels faster in non-air mediums than blue light because of its wavelength, but I'm not understanding why this doesn't happen in a vacuum? This is related to the topic of dispersion and the change of index refractions with wavelength. However, I'm not understanding why this happens. All I know based on educational materials that the index of refraction increases for colors with higher frequencies or lower wavelengths, ie. blue travels much more slowly.
In fact your statement is not quite right: air does disperse light - its refractive index does depend on frequency, albeit very weakly. If you replace "air" with "vacuum" in your question, then the statement you are asking about is a correct one.
Dispersion arises from the interaction of light (an electromagnetic field) with the electrical charge present in the atoms of the dispersing materials.
In air, there are far, far fewer atoms per unit volume than do materials we think of as dispersive. A vacuum, by definition, has no electric charge at all for the light to interact with. Therefore, its refractive does not depend on frequency. This last statement is true because (1) light is mediated by a massless field and (2) special relativity requires that all such fields propagate at exactly $c$.