Source is Part III § 2 of the US flag code enshrined by 4 U.S.C. § 5.
On the admission of a new State into the Union one star shall be added to the union of the flag; and such addition shall take effect on the fourth day of July then next succeeding such admission.
This isn’t legally binding – you can fly a US flag with five stars representing the CCP and its four governed social classes if you want. But it does represent official federal guidance on the design of the US flag. So if Washington, D.C. were added as a state, you wouldn’t see the 51st star appear on federal buildings until the subsequent Independence Day.
✨ Not constitutional ✨
But for merging? Theoretically legal. Never happening in practice. (For small states, who’d be the likeliest to have a reason to merge, you’d completely fuck your Congressional representation. You’d have to sort out a mountain of laws to merge, throw away, etc. All states wanting to merge and Congress would have to approve. You’d probably spend decades messily unifying infrastructure. I could keep going; there’s no realistic circumstance.).
I don’t see any provision for it, so I assume – between secession being repeatedly, handily struck down as unconstitutional and merging being so unfathomable – that it’s easier to just make something up ad hoc (or go by the addition rule) if any states ever merge.
I was thinking a bit ahead. Once the GOP loses the midterms, Trump is probably going to send in the natl guard to several states, proclaiming “the election was stolen.” He will go far beyond the threats of the last lost election. Since the army is, already fully intimidated, dancing to trump’s flute, a few states and a few generals may well unite and decide enough=enough. Then the second civil war will start, for the same reason as the first one (1861-65): secession. And ultimately a couple of stars may well need to be removed.