Isn’t it actually against the law/constitution to wear the flag as clothes?
No. It’s against flag code, but there is no real law or enforcement of the flag code. If you do break it, I will immediately assume you are not a patriot and instead you are a nationalist because you didn’t take the ~5 minutes to look up the flag code.

I don’t think patriotism and flag code are necessarily linked.

Example

Military veteran detained after burning American flag in protest at Trump’s executive order

The Independent
Flag burning isn’t against the flag code. Flexing your 1st amendment is definitely patriotic.
Huh, TIL. I guess throwing it on the ground was against flag code but not the actual burning.
The burning after it touches the ground is actually what you’re supposed to do according to the flag code.
That, I also learned, is a common misconception. Flag code just says pick it up off the ground.

You’re correct

Contrary to an urban legend, the flag code does not state that a flag that touches the ground should be burned. Instead, the flag should be moved so it is not touching the ground.

I guess just if it gets tattered you’re supposed to dispose of it properly.