That's not the date of the vote. That's when the bill was first introduced.

https://en.wikipedia.org/wiki/Flag_Desecration_Amendment#Proposed_amendment

On Monday, June 26, 2006, the Senate began debate on the proposed amendment. The following day, the amendment, sponsored by Senator Orrin Hatch, fell one vote short in the Senate, with 66 in support and 34 opposed.

The proposed amendment said simply: "The Congress shall have power to prohibit the physical desecration of the flag of the United States."

Before the final tally, the Senate voted 64 to 36 to reject an alternative measure designed to provide political cover for those who opposed Hatch's legislation. The measure -- a proposed statute, rather than constitutional amendment -- was offered by Sen. Richard J. Durbin (D-Ill.) and was strongly endorsed by Sen. Hillary Rodham Clinton (D-N.Y.), a possible presidential candidate who has sought a middle ground in the flag-burning debate.

The proposal would have outlawed flag desecration if the perpetrators were also damaging federal property, trying to incite violence or trying to intimidate someone. Opponents called Durbin's measure a political fig leaf that the Supreme Court would rule unconstitutional.

Notice the word "before" in there, as in, the vote for Hillary's bill happened before the vote for the amendment. Not that it really makes a difference. For all your high-horse condemning about facts and "fake news" you don't get the facts right, instead you simply lie by saying Hillary wrote this bill and then voted against it when she obviously didn't.

I value honesty and facts

Then why are you insisting she voted against this bill when she didn't?

Trump's tweet for revoking citizenship has no minimum and says nothing about damage or violence

Trump's tweet wasn't a bill, it was him giving an opinion in under 140 characters. Again, you pretend as if the minor variations in these two things are what makes the difference, but that's only to protect your own hypocrisy. This bill obviously doesn't mean "if someone commits an act of violence that would cause him or her to be imprisoned for a year anyway, and happens to be burning a flag in the process, then they may go to prison for a year." This is adding a heavy degree of consequences (jail time) for burning a flag.