What's the difference between an aura and a chakra?
The aura is supposed to be the field that surrounds your physical body. Whether it's generated by the physical body or not depends on who you ask. Kirlian photography, for example, uses galvanic skin response to take the pics, while 'seen' auras are not supposed to be seen with the eyes. So it all depends on what tradition you are coming from. Eastern mysticism used to see the aura as a precursor to the physical, but I don't know if this is the case anymore.
A chakra is a vortex of energy that acts as a transducer, in that it exchanges energy from the physical to the metaphysical. It is an in/out system, if this makes any sense. You could say that the chakra is part of the energy body and the aura is a reflection of said energy body, but this is just extrapolation.
Is the analysis of auras, Western occultism considered part of Kundalini Yoga or chakra analysis?
I'm not sure what you mean in this question. Western occultism (such as Theosophy, for example) borrows both eastern theories (such as energy bodies, Kundalini and some terminology) with ancient egyptian ideas or ideas attributed to ancient egypt and greek metaphysics, such as the Emerald tablets of Hermes (greek)/Thoth (egyptian) for example.
Sylvia Plath explains that aura analysis can allow a witch to open your door when sleeping.
I suppose that if you study the aura in such a way that you can find a 'weak spot', and you believe that the aura is somehow a 'protective coating', that you could believe something like that- I have heard/read that influence happens when you entrain your vibrations to the aura of another person, and in such a way make them influenceable- I don't know if any of this is true, but if I were going to go with 'protective coating' vs. 'entrainment', I'd go with option #2, only because it makes more sense to me, provided this is true.
I don't think that you can 'open' a 'door' to another person, unless you know their psychology and can exploit it. But that's just me, I suppose.
How about chakras? (There is a wing chakra on an angel that is analyzable. What is the wing chakra called?
I wouldn't know, I bet Aunt Clair does.