"I hope to have God on my side, but I must have Kentucky." - Abraham Lincoln
Alas for the CSA, Union sentiment was generally stronger in both states, particularly Missouri. Short of something truly outside the box, you would need a POD very, very early to have any chance of accession of Kentucky. Missouri really would be impossible, save for a possible partition.
Bragg's and Kirby-Smith's invasion even seems too late in the game; by that point, majority sentiment seems to have settled with staying in the Union, which out-recruited the CSA in Kentucky. Polk's violation of Kentucky neutrality first didn't help; at any rate, southern sentiments were strongest in Jackson Purchase and the western part of the state, which unfortunately was never reached by the 1862 invasion. Yet I do think that there was enough fluidity in the first months of the war that there's a chance to swing secession sentiment just enough if the Union precipitates actions that outrage public sentiment there. Say someone more hotheaded than Anderson - preferably a potent combination of viciousness and incompetence, perhaps along the lines of Fremont - is sent to deal with Kentucky, and violates Kentucky neutrality almost immediately, commiting atrocities against civilians (i.e., the kind of treatment dished out in much of Maryland). Magoffin might - might - then gain enough support in the legislature to push an ordinance of secession. But even then, there would be a large Union sentiment at large in the state, focused on Nelson's Home Guard, and limits on Confederate logistics and power projection would still require a very early CSA victory to secure the state.
Missouri simply had too many Germans, Irish, and free soilers in St. Louis and the east of the state, and the CSA government absolutely zero ability to put any forces into the state. Confederate sentiment was mostly in the Bootheel and the Southwest, stretching up to the Kansas City area. It would take a pretty massive departure to even manage a partition of the southern parts of the state.