No, because he’s violating the rules of his workplace.
If you want to stop flag burning, make flags out of fire resistant material.
I can think of no greater symbol of exactly how great America is than a citizen burning an American flag. I can also think of no greater symbol of the dangers to American freedom than an amendment to the constitution to ban that act.
The fact that as an American citizen you can, without risk of imprisonment, burn the flag of your country in protest to your government is a testament that we as a nation believe in freedom so much we are willing to allow such an act to take place.
But more to the point - this is a political BS vote. There’s no outbreak of flag burnings going on across the country. It’s a cheap and easy way to make an attack ad. “My opponent voted for flag burning” there 5 seconds, but it takes more than a 5 second sound clip to make those who oppose burning the flag on a legal level understand just how important the right to burn that flag is.
Because something isn’t popular or people don’t want to hear it is sometimes what makes it so important.