Neji's close range and hand speeds are incredibly fast with his pinpoint accuracy and devastating eight trigrams attacks. He only needs to stay in one spot and use spinning motions to help defend against kakashi's taijutsu.
You pretty much just described a typical hyuga's fighting style, which is what I have already factored in. Neji is not hitting kakashi without receiving a raikiri or an even more serious blow.
Kakashi 's taijutsu is most likely not better than lee's since lee has trained taijutsu his entire life and has opened many more gates, a feat that only true taijutsu virtuosos could accomplish.
Manga states kakashi is better at taijutsu than lee is. As of now, we have only seen lee open 5 gates and we don't know how much kakashi can open, so saying lee can open more than kakashi is not concrete.
Next, lee only started training in Gai taijutsu once he became a gennin, before that even his taijutsu was just decent. Kakashi has been training in taijutsu far longer than lee has.
Neji's taijutsu is considered to be the most deadly and he is also a master of it.
Okay... so he will beat 7 gated gai also since his taijutsu is the most deadly
I am in agreement with the sharingan part, but it does not mean that he automatically wins in close range since it is what both neji and lee specialize in.
sharingan predicts movement. Naruto was blitzing sasuke at the valley of the end, naruto had way more speed than sasuke did, but once sasuke gained the three-tomoe sharingan, he started wooping naruto, despite naruto's massive speed advantage.
In this scenario Kakashi has both the speed advantage and sharingan. These guys will not hit kakashi without kakashi hitting them twice as much and twice as hard, and that is being generous.
Also he necessarily doesn't need to use rotation for kamui, since it is only useful for warping away objects that are moving in a linear fashion.
Yet a jump is horizontally linear, and vertically predictable. But I have to admit that kakashi has never kaitened a person in mid-battle before, so I say that he won't kaiten neji and lee if they are constantly pressuring him up close with taijutsu.
The best advantage kakashi holds is not only his speed/reflex/battle perception advantage over neji and lee, but he also has long range jutsu, and jutsu that will eat up taijutsu fighter:
i.e. raiton clone