Question and formulation aren't that bad but sure has fundamental problems in it.
A proper answer is rather long and will require a lot of clarifications and discussions and it is not what SE is about, even if we do not dive in howtos, and that was intended to be a comment, but it does not fit and it possible to make some meaningful response. If you wish shed more light on the problem you migth contact me at discord
Armor and problems
To some extent such armor is possible, however, some elements do not fit as you described them, some are not such a problem as you expect them to be(that heat thing, napalm etc), some will work(they have to) differently and not necessarily will fit in your expectations and narrative and scenarios of actions you imagine.
But there are 2 points to highlight as tldr for such an answer
- first you can't make such armor with passive means just like a hard resistive barrier - in the case of antitank missile as an example - you have to do some preemptive actions to keep the soldier alive and well. It just because of physics - as the missile has enough energy to accelerate the solder with accelerate ratios which will lead to inside damage of his biological component.
It not necessarily so, as armor, one of its parts which we may think like an interface, can be embedded in the human body, increasing resistance against acceleration and other potential factors which may cause physical damage to human body. So as it can be part of the system which repairs those damages if they happen.
So then maybe it will require lesser preemptive actions, and it may look like as if it was acting passively, but in reality mechanics behind it will be quite complex.
A second point to highlight is
- the technology which may make such armor possible can be used as a weapon too
So it basically only fits scenarios more advanced fraction against currently existing technologies.
Another side problem is that such technology makes use of the solder needing protection - not necessarily, and soldiers are not likely to be used in a conventional way at least. So, focusing on answering one question you rather bring bigger inconsistency of different sorts.
General advice in your situation is to handwave, so you will have more chances to keep consistency in the logic of your story.
What it can be
But as for to gain some confidence in terms of - if similar armor is possible at all - it needs to think about it in terms of smart matter, some 2d nanomaterial made of carbon nanotubes stuff - strains - which can move relative to each other. So those are threads 0.1-1um in diameter and from cm to hundred meters long, which are controlled by some program to weave different parts of the armor.
To some extent those anime characters with their energy based systems when they cry activation transformation - when their outside morphs in something fancy - they can be considered as characters wearing some sort of such armor. (and btw nobody tries to justify it in terms of real engineering, as little as I'm aware of that genre, and seems people do not care that much about that; so you can do the same)
Carbon nanotubes are recognized as one of the robust materials with a tensile strength of 100+GPa, and the ability of threads to slide against each other allows to create interesting effects, not necessarily just static change of shape like making 0.5m "pillow" in front of a solder in anticipation of some missile to collide, but also some dynamic protective layer like tentacle which destroys the missile at 50m distance.
Flight is possible, fast heat dissipation if there is a cold atmosphere in reach of a suit(which may be 100 meters, so as 100m up) or another cold end it can find(ground in some cases). It won't be possible to stick anything to the suit, worst case scenario it will lose a 0.1-1um layer of material in the spot.
Burning won't be a problem for it even if it made out of combustible material, because it can use grains of surround materials or which is part of the equipment to create protective layers as it naturally forms in terms of passivation layers, or oxidized layers like aluminum one has and it can have explicitly fast surface heat dissipation capabilities - sou that you can have acetylene torch pointing at some spot on it and it won't heat a bit(not exactly but it complex..)
Feasibility of base technology
The technology - carbon nanotubes as sliding elements - it very close to carbon artificial muscles technologies which some institutes try to create. There are some physics which may make it possible, actually at least 2-3 options I may recall atm. So potential in terms of feasibility if hight, but surely we do not have that material yet.
It was applied, the same material, to a different scenario here, look for a section which starts with "Note about Venus scrap, snake elephant" I tried to depict some potential science.
So as later I got some interest in the technology(questions about it) and there are few articles with clarifications, which also may be helpful if you try to adopt that they go under tag smartmatter here
Generally, you should understand that it(potentially) quite a complex piece of technology and probably not that useful in therm of your storytelling so it not necessarily the droids you are looking for.
At the same time, I have reasons to think that armor with similar properties you probably describe is physically and technologically possible.