Republicans would need control of at least 34 state legislatures to be able to call such a convention, and 37 to ratify any amendments.
So far they have unified control of 31 state legislatures. Of those 31, 19 have signed onto an application for an Article V Convention put forward by Convention of States, a conservative activist group.
https://www.businessinsider.com/constitutional-convention-conservative-scholar-states-2022-8
https://www.businessinsider.com/constitutional-convention-conservatives-republicans-constitution-supreme-court-2022-7
It's interesting that MLK said the whole "arc of history" thing. He of all people understood how justice doesn't just happen, it's something fought for.
Kind of weird for him to pull out the whig historiography when he of all people knew how historically wrong it was. Like chattel slavery died out with the Roman Empire and then got brought back by bloodthirsty Christians to fuck over West African people in particular. That long arc of history most certainly did not bend towards justice.
If you think you can win your struggle, it helps to tell people that victory is inevitable. To quote Eugene Debs, "You can accelerate [socialist revolution] or removed it, but you cannot avoid it."