Probably not much at first.
Kentucky is unaffected because she was never a Territory, but remained a part of Virginia until her admission as a state in 1792.
OTL, Tennessee was briefly a Territory after her cession by NC, but TTL this probably won't happen, and TN will pass directly to statehood as KY did.
That only leaves the areas which later became Al and MS. However, in 1787 these still belonged to Georgia, and weren't ceded until 1802. Personally, I'd be very surprised if this cession weren't made conditional on the continued legalisation of slavery there.
The $64,000 question is what happens in Louisiana. The French will want some guarantee for the slave property of their nationals, but those are mostly in and around New Orleans. So there's at least a chance that the rest of the Purchase, including the future State of Missouri, may remain free.
These are all good points. However, the precedent has been set to stop the spread of slavery. Furthermore, slavery did not become a real issue threatening constitutional government until the Missouri Compromise. In this scenario, at the very worst, Missouri and Arkansas will never become slave states, and possibly others as well that were part of the slave bloc.
It is also possible that with the push that the forces against slavery are emboldened and have the wind behind their backs. Just as slavery was steadily abolished in the northern states where it is legal, new states that had some slaves - like Kentucky or Tennesee - might end up quickly abolishing them as well since their initial slave populations are likely to be low. Even Virginia might abolish it.
This greatly reduces the ability of slaveowners to dominate national politics and control the agenda on slavery for a long time. There is bound to be blowback at a certain point once the cotton gin revitalizes the importance of slavery, but by then the die will have been cast. I could see a crisis involving South Carolina similar to the nullification crisis of 1832, but threatened secession will be seen as suicidal, and South Carolina will not have the support it eventually did in 1860.
Ultimately, I see slavery becoming more and more restricted, and its concentration in a few southeastern states will be seen as a strange anomaly. At some point abolitionists will seek its outlaw even down there, but after some harsh words, compensated emancipation will likely happen - perhaps by the 1880s.