Hello, Dena -- welcome to the forum!
There are several threads in the "American Flag Disposal" section of the forum that discuss this topic. My personal opinion, which I've expressed a couple of times here, is that cutting up the flag is rather grotesque -- it's more like some kind of weird pagan ritual than anything patriotic.
For what it's worth, the original version of the US Flag Code that was adopted in 1923 said:
"When the Flag is in such a condition that it is no longer a fitting emblem for display, it . . . should be destroyed as a whole, privately, preferably by burning or by some other method in harmony with the reverence and respect we owe to the emblem representing our country."
The "as a whole" part has been dropped from the current version of the flag code, but it is still in some military regulations. The Navy NTP-13B says:
"When the national ensign is in such condition that it is no longer an acceptable emblem for display, it shall not be cast aside nor used in any way that might be viewed as disrespectful. If it is not preserved, it will be destroyed as a whole, in private, preferably by burning, but in any case by some method lacking any suggestion of irreverance or disrespect to it as the national emblem. This destruction should be complete to the extent that no part remaining is recognizable as once having been a part of the national emblem."
The comparable Army and Marine Corps regs do not include the "as a whole" provision. They do, however, say that it should be done in private rather than in a public ceremony.
Best,
Peter Ansoff