Kansas is pretty much a non-starter. For it to be a secessionist state, you'd need to have a POD going back to 1854, if not earlier. By the time the war ended, the place was a rabidly radical abolitionist stronghold. As already pointed out, Kansas sent a huge proportion of its men to fight for the Union and they developed a reputation as some of the most ferociously anti-Confederate units in the army, too.
Missouri and Kentucky are both doable. IOTL, both were quite divided and contributed tens of thousands of men of the Confederacy (the Orphan Brigade of Kentucky troops and Cockrell's Missouri Brigade were arguably the two best Southern brigades of the entire war).
The unilateral emancipation proclamation issued by General John Fremont (then commanding in Missouri) in late 1861 was very nearly a disaster for the Union. Had Lincoln not handled the matter so adroitly it might have pushed either or both of the border states into secession. Then you have General Leonidas Polk, who stupidly crossed the border into Kentucky to occupy Columbus in October of 1861, thereby making the Confederacy the first to violate the state's declared neutrality. Fremont was even then planning on moving into Paducah, IIRC.
If Fremont and/or Polk (or perhaps Davis, who might have decided it was stupid to appoint Polk to an important command) had done things just a little, then Kentucky and/or Missouri could have ended up seceding. The former is more likely than the latter.
Missouri would have been reconquered, as it would have been very difficult for the South to project force into the region. Kentucky, on the other hand, had more fence-sitters who joined the Union IOTL who might have sided with the South ITTL. Missouri was more strictly divided into pro-South and pro-North sides, it seems to me.
I do agree with Lincoln, though. . . to lose Kentucky was to lose the whole game. If Kentucky seceded, the South would likely have gained its independence.