When Iron Man flies he is shown with fire coming out of his feet just like a fuel-propelled rocket.
Where is the combustible material generating the fire coming from? Does he have a fuel tank? What is his operative range?
Since your images are from the film Iron Man, I'll initially address that universe. In the film canon, Tony constructs a miniature Arc Reactor and implants it in his chest. This provides a fantastic power source for the armors he later builds. In the Mark 2 & 3 armors, Tony uses his Arc Reactor to power repulsors (a fictional technology that uses energy to generate thrust), which his suit contains on the palms and feet (per Wikipedia). The repulsors on his feet provide the thrust you see in the images in the question, while he uses his hand repulsors and flaps on his suit to provide steering.
In the comics, it's decidedly more complicated, but modern Iron Man armors utilize repulsors, like the film version. Older iterations of the armor did use chemical propulsion (i.e. rockets). You can read an extremely thorough listing of his past armors on Wikipedia.
The thrust is generated by the electrical device which keeps him alive and powers his suit.
My expectation is that it is something akin to an Ion thruster:
An ion thruster is a form of electric propulsion used for spacecraft propulsion that creates thrust by accelerating ions. Ion thrusters are categorized by how they accelerate the ions, using either electrostatic or electromagnetic force. Electrostatic ion thrusters use the Coulomb force and accelerate the ions in the direction of the electric field. Electromagnetic ion thrusters use the Lorentz force to accelerate the ions. The term "ion thruster" by itself usually denotes the electrostatic or gridded ion thrusters. Ion thrusters create very small levels of thrust compared to conventional chemical rockets but achieve very high specific impulse, or propellant mass efficiencies, by accelerating their exhausts to very high speed. However, ion thrusters carry a fundamental price: the power imparted to the exhaust increases with the square of its velocity while the thrust increases only linearly.
Because Tony Stark is a brilliant inventor he was able to create a non-conventional electrical power device (electro-magnetic arc reactor) which is not constrained by the size and weight limitations of conventional technology.
The answer is simple, its called a VASIMR which is much better than the ion thrusters, tony probably used ion thrusters but a technology which we know today is a VASIMR rocket, similar to the ion, uses electricity and a gas, the gas is ionized then turned to plasma which heats up between 1.8-3.7 million degrees depending on how you use it, it can either act like a ion thruster or a rocket propelled thruster. The advantage of the VASIMR is the very low fuel consumption. The gas used is hydrogen, an advanced suit like the iron man can simply extract the hydrogen from the air through electrolysis, the water is condensed as the suit pressurizes ram air to form water, the hydrogen gas is produced and directly sent to the rocket boots AKA VASIMR.
Here's the link which explains the VASIMR
In the suspension of reality you can generate more than enough thrust if you are willing to release the nuclear bonds of the atom. At issue would be the resultant radio activity. You would mitigate this by controlling the nuclear reaction so that it would not release any unstable isotopes. The resultant heat energy would be then used to propel the resultant new atomic structures. Even a small amount of material would potentially have sufficient thrust if propelled fast enough. Remember it only took a few kilograms of uranium to produce the first atomic bomb. E=Mc^2 y'all
My theory of Ironman's jet boots is that he uses ion thrusters, which acts like suitable replacement for jet thrusters. I think he ,also, used a metal which is a bad conductor of heat.
My idea is a bit radical I think Tony's suit might have a mini super cooling device which separates hydrogen and oxygen and liquefies it to produce the reaction that causes the thrust.
The arc reactor powers the thruster to make a large amount of thrust. You can use solar panels to power the suit, but it might fail to produce enough power in time. Or you could make a mini sun to power it.
Tony Stark take an electromagnet at his chest and this saves him from the bomb's tiny particles in his heart. This electromagnet generate electromagnetic waves and he gives thrust to his suit by burning hydrogen.
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