No, burning a book is not the same thing as burning a flag.

[howard112211]

Both are symbolic gestures with different meanings. To say they are the same is akin to saying that a swastika is the same thing as a mandala. The message matters. Burning a flag is usually an anti-nationalist or anti-authoritarian gesture. Sometimes also a rallying gesture in national
warfare. Burning a book usually means something different. Usually it is implied censorship together with an implied threat to the books readers
and/or authors. Arguing that both are the same thing, just because both are protected forms of expression, is rather silly.

[baldguy]

1. The difference between enforcing oppression vs fighting it.

[lunatica]

2. I think they're both a grab for attention more than a protest

Although they are a protest. But to what end, and for what purpose? That's the silly part. People get all emotional and outraged over the destruction of the material manifestation of ideas, as if the ideas themselves are being burned. Burning religious icons doesn't kill the religion just as burning the flag doesn't do anything one way or the other to the country or its policies.

[dkf]

3. Depends where it is being burned and who is doing the burning.