Answer: No, a Flag does not have to be destroyed if it touches the ground.
This common misconception stems from the widespread belief that compromising the flag in any way at all immediately tarnishes it, rendering that particular flag unsuitable for display. Of course, the flag should be treated with the utmost respect and care at all times. This is a given. But it is acceptable to wash or even dry-clean the flag to restore it to a state worthy of display.
This is not to say, however, that there are not stringent guidelines that outline the proper way to display the flag. According to the U.S. Flag Code, the flag must be “hoisted briskly, yet lowered ceremoniously.” When regarding the flag, the symbol of the unity of our nation, submission to the flag’s magnitude is expected. For further reading and confirmation, please refer to the American Legion’s post on this subject.