Many psychics claim to be able to see auras. Many healing methods like reiki are based on them.
I don't think Reiki is based on the concept of auras. As far as I know, orthodox Reiki doesn't use the term "aura". I searched a few Reiki ebooks I found online and they don't include the term. Reiki is a framework created by a Japanese Buddhist named Mikao Usui in 1922.
Japanese takes aura as a loan word with indicates that Japanese does not have a native equivalent.
Psychics claim that if you look at someone with soft eyes, you can see a hazy field around them, white at first, which with practice becomes colourful and more detailed. They claim this is the aura.
I would judge that claim as true. In principle, you can get people in a state where they see strange things. Drugs like LSD help, but you can access states where people are suggestible for visual hallucinations also without drugs. One of the most detailed well-documented descriptions of hallucinations I have come across are tulpas where people with mental training see people who are just as detailed as real people.
If we move back to the soft eye thing, that normally gets you a counter color. If you look at a red circle, that circle will have a green glow around it. Purkinjes Vision - The Dawning of Neuroscience describes a bunch of related effected in the chapter about halos and afterimages.
If I understand right, aura training begins by convincing the person that auras are real by showing them some of those well-documented Neuroscience halo effects. Together with a highly meditative state and social pressure that's enough to get a bunch of the people who try to hallucinate more complex images.
That leaves the question of how the colors of the people come about. During the time the people are in a suggestible state they are going to be told what colors they are supposed to see in what circumstances.
Different brains will draw on different information to process that information into an aura color that's consistent with suggestions.
An aura is claimed to be a physical field:
The strongest energy source of the human body is the human heart. You can measure it via EKG. Depending on the strength of your measurement equipment you can measure it from a bit of distance. I think it's unlikely that humans can directly perceive the EKG of another person they don't touch.
There are however indirect way to access that information such a slight pupil dilations.
At that point it's useful to remind of Ekman's micro expressions that can last on the order of 1/25 to 1/15 of a second. There are all sorts of information that we perceive on a visual level and that get processed by most people on a unconscious level.
Humans can't smell as well as dogs who can be trained to detect some cancers via smell but there a lot of information that's available through human senses that isn't organised in a form where it's useful and which potentially can be put in a form through training.
It could certainly by useful to pull that kind of information together into a color spectrum to interact with it better.
The memory championships get won by people who rearrange information through mnemonics in a way that helps them to achieve extraordinary results. As far as I understand current record holder usually use face memory of human faces and spatial memory to encode information about playing cards. Recombining human senses, can certainly achieve useful effects but you won't know what individual people who try it can do.
Humans also radiate heat waves via infrared. That effect could be strong enough to be perceived by other humans. Heat is interesting because outer body extremities with low blood flow are colder than those with high blood flow. It plausible that a part of the body that doesn't get enough blood flow is physically ill and therefore has a "weak aura".
Given that a lot of energy healers do work with relaxation and tensions can restrict blood flow, a bunch of what those people react to can very well be heat.