Burning the flag is awful, ungrateful, and unpatriotic...but it's not #unconstitutional. Flag burning continues to be protected as free speech by the U.S. Supreme Court, as it should be since the flag itself represents "freedom".
The U.S. flag is sometimes burned as a cultural or political statement in protest of the U.S government. The 1989 Supreme Court decision in Texas v. Johnson ruled that it is unconstitutional for a government to prohibit the discretion of a flag, due to its status as "Symbolic Speech." To do so would be a violation of the first amendment's protection of free speech.
In his ruling for the 1989 decision, the late Supreme Court Justice Antonin Scalia stressed that flag burning is protected by the Constitution. In other words, protecting freedom from government overreach is more important than any symbol – even the American flag. Personally, Scalia abhorred flag burning. Why didn't he vote to outlaw it? Because "I am not king," he said.
Making flag burning illegal would empower the government to engage in thought control...a scary proposition. There is a distinct difference between real and forced patriotism.