In the name of Allah, Most High and The Beneficent.
And Blessings on All of His Prophets.
Elhamdulillah for the first answer and clarification where I would just like to add few scientific explanations and share a few thoughts in this answer of mine.
When the stars are mentioned in Qur'an Kerim 67:5 as Missiles, we can see this Fact for true:
How does this look like?
"And the sun runs [on course] toward its stopping point. That is the determination of the Exalted in Might, the Knowing."
Qur'an Kerim 36:38
Our Sun is one of the fastest if not The Fastest thing in our solar system, moving at estimated 225 kilometres per second if not even 300 KM/S.
So yes, Our Sun Is The Missile.
Our Sun literally orbits the galactic centre of the Milky Way with each orbit of around million years long or so.
"He is the One who has created the night and the day, and the sun and the moon, each floating in an orbit."
Qur'an Kerim 21:33
Since there are trillions if not googol stars in our universe, just count how many Missiles that is.
Now how Stars are affecting the devils or being thrown at them?
"Beyond Low Earth Orbit, space radiation may place astronauts at significant risk for radiation sickness, and increased lifetime risk for cancer, central nervous system effects, and degenerative diseases."
These are only some challenges that space farers face when travelling the universe.
At higher enough concentrations, Radiation can vaporise nearly everything; there's no known material known to us that can withstand against it.
That's why nuclear weapons used on Hiroshima and Nagasaki created so much thermal radiation that it simply vaporised people and buildings.
You know about Gamma Ray Bursts and how they could destroy life on Earth if they hit close enough.
If you have read about the Chernobyl nuclear disaster, you'll find that Soviets used robots to shut down the so called Elephant Foot inside of reactor and failed miserably since the radiation fried the machines' electronics and if it was in even higher concentration, it would burn everything.
According to the NASA's link I've provided, the further or higher into space you go, the cosmic radiation becomes stronger and it will affect everything and everyone.
If it has long term detrimental effects on humans, how hard it hits the jinns?
The Ayah in question refers to specific evil Jinns (devils) traveling to the region where Angels dwell to spy on Divine Messages and to return back to Earth to tell it to the soothsayers.
As we know the story, since the Muhammed SAWS became The Prophet, everybody was banned from this eavesdropping.
Now, how far this dwelling place of Angels is from Earth?
Googol or who knows how many light years.
The longer the space travel, the longer you are exposed to cosmic radiation and you'll die.
That's one possible way explanation by our feeble human minds and knowledge but how are these stars being thrown at the devils?
The closer elucidation we might find in Qur'an Kerim 72:9
"We used to take up positions to listen in; but whoever listens now finds a Projectile In Wait For Him."
This could mean that spaceships or traveling vessels of jinns are being intercepted in some manner by the stars and destroyed.
Now, from our human perspective according to our limited knowledge, all Allah (SWT) could do to stop eavesdropping by the jinns is to only increase the levels of cosmic radiation around the dwelling place of Angels and in that case:
Nothing, absolutely nothing, no biological nor mechanical organism could approach.
We don't count Angels here since they are certainly of more higher and better DNA structure to better handle it then the others.
For example, cockroaches are known to be "impervious" to the radiation in very short time periods.
They simply shed their skin off and continue with their life.
This is why the term Burning Flames can easily refer to the radiation.
Since the science is 95+% based on theories, I wouldn't rely too much on science in proving of the science of Higher Being, The Creator, the things that I've mentioned (and few others ) are based on real life observations (very rarely used manner in which our science explains things),
This is our human supposing based on our extremely limited knowledge on cosmos and the laws which Our Lord, Allah (SWT) has set,
And Allah (SWT) Knows Even Far Better,