As a political movement, the Know Nothings practiced a studied ambivalence on the topic of slavery. They drew their support largely from conservative Whigs who did not trust abolitionists on the one hand, or secessionists on the other. Institutionally, their choice was not to have a position on slavery. In practice, northern Know Nothings tended showed greater hostility to the institution than their southern counterparts did. Northern Know Nothings typically acknowledged the right of white southerners to own slaves, but were in no great hurry to see it go away, though you can find examples of northern Know Nothings more outspoken in their opposition to it. Southern Know Nothings, likewise, wanted to keep slavery legal, but they shied away from the more extreme rhetoric of proslavery apologists, and did not want to advocate for it at the expense of the Union. One of the reasons the party did not last longer than it did was because it could not take a position on the dominant issue of the day: slavery. By the time of the presidential election of 1856, the American Party, as it was officially called, had more or less become a re-branded Whig Party, a party committed to Unionist nationalism, bourgeois social values, and indifference or muted hostility to slavery
On the issue of secession, the Know Nothings were generally opposed to it. By the time secession became a ripe issue in the winter of 1860-1861, the party had ceased to exist as a functional unit, having divided on the slavery question. Northern Know Nothings seem to have found their way into the Republican Party, where they formed part of the new party's conservative wing. In the South, Know Nothings either departed from formal party politics, or took part in locally-run parties opposed to the program of more aggressively pro-slavery southern Democrats, such as the pessimistically named Opposition Party that formed at the end of the 1850s. This formed the core of the Constitutional Union Party in 1860, a party for politically homeless southern Unionists whom the party politics of the day had let behind. North or South, those involved in the Know Nothing movement were opposed to secession more often than they supported it. Drawing on their Whig nationalist heritage, they saw secession as a dangerous, revolutionary, and unwarranted step.
Readings
Tyler Anbinder, Nativism and Slavery: The Northern Know-Nothings and the Politics of the 1850s
Darrell Overdyke, Know Nothing Party in the South
William Gienapp, The Origins of the Republican Party
William Hitchcock, "The Limits of Southern Unionism: Virginia Conservatives and the Gubernatorial Election of 1859"
Bruce Leving, "Conservatism, Nativism, and Slavery: Thomas R. Whitney and the Origins of the Know-Nothing Party"
John David Bladek, "'Virginia is Middle Ground:' The Know Nothing Party and the Virginia Gubernatorial Election of 1855"