Why do you need 'האם'? Isn't the question mark enough?
You don't. Yours was wrong because you wrote הטיסה הזאת which is "is this flight..." and that is different to זאת הטיסה "is this the flight...".
ha'ím zot ha-tisá le-artzót ha-brit?
Since they introduced abbreviations, why not use them?
Is this also correct?
האם הטיסה הזות לארצות הברית
No, two reasons:
It's הזאת not הזות.
Yours means "is this flight to the United States", not "is this the flight...".
I've forgotten. When do you use זו in a sentence?