Because I do not think legislative history matters very much in determining what a constitutional provision objectively means, I would not, on those grounds alone, limit the First Amendment to the three items mentioned. Legislative history is useful only in so far as it gives us insight into the public meaning of the words.
In general, I would tend to agree. It so happens in this case that I could not find anything other than legislative history.
I researched the constitutions of the various states on this issue before making my earlier post, in the hope that they might shed light on the issue. Unless I missed it, the only state constitution that provided for the freedom of speech was the constitution Pennsylvania (which protected speaking, writing, and publishing). As for the others: at most, the freedom of debate in the legislature and the freedom of the press were protected (as in English law).
On the whole, the deciding factor should be the fact that under such a law, the flag can be flown "only in one direction," as Justice Scalia put it. One can honor the flag in any way one pleases, but one is not allowed to dishonor it. One is allowed to respectfully dispose of a soiled flag by burning it, but one is not allowed to show disrespect by desecration. On the whole, it is not the mere act of flag burning that is being punished--it is the expression of one's disrespect for the country. I'm sure that the First Amendment would cover the situation.
Poll
