Impossible to know.
But my guess is that slavery would have continue to grow for a while, particularly in states south of the Mason Dixon line and any states affected by the Missouri Compromise. meaning that most of the Western US would have been open to (or legal) to keep slaves.
Now, slavery was really only useful in Southeast, where there was a good deal of rainfall and water and slaves would be useful in agriculture. Once you get west of Texas, and to some degree NW of Missouri, the climate (and agricultural potential) changes markedly. You can’t have a cotton plantation in Colorado or Utah, for example.
But the advent of tractors (and picking machines, and especially the internal combustion engine) would have spelled the end to manual agriculture and the need for slaves.
So in my estimation, slavery would have died out by around 1925–1930 of its own accord. And if it hadn’t by the time of the Depression, the Depression would have ended it for sure.