A co-sponsor of the latest resolution to ban desecration of the Stars and Stripes by constitutional amendment, the otherwise liberal California senator Diane Feinstein, cited once a 1974 opinion by Justice Byron White:
“It is well within the powers of Congress to adopt and prescribe a national flag and to protect the unity of that flag . . . The flag is an important symbol of nationhood and unity, created by the Nation and endowed with certain attributes... There would seem to be little question about the power of Congress to forbid the mutilation of the Lincoln Memorial or to prevent overlaying it with words or other objects. The flag is itself a monument, subject to similar protection.”
This analogy is profoundly faulty. Note that unlike the Lincoln Memorial, "the flag" has no address. Were we talking about something physical, then "the flag" is a constantly changing number of pieces of fabric anywhere and everywhere. So banning flag desecration is more like banning mutilation of a souvenir replica of the Lincoln Memorial that you bought at the gift shop. There would seem to be a little question about the power of Congress to forbid that.
But the Stars and Stripes isn't physical, it's an unpatented design. When a flag is desecrated, a modified or adapted design is created, in the way editorial cartoons are created by modifying or adapting the likenesses of presidents. A ban on desecrating flags is simply a ban on criticism, which has no place in the U.S. Constitution.