Please let us know your flight timing/timings. Neither is accurate.
"Please let us know the time of your flight" is accurate.
If you were to say, "Please let us know your flight time", this would not be accurate because the sentence could mean "let us know when your flight will leave/arrive" or "let us know the length of your flight.
If accuracy is what you are aiming for, then I believe that my first sentence is the most accurate.
Sentences 2 and 3 are OK.