There's no evidence that Jackson taught his slaves or anyone else's slave to read and write. He did teach a Sunday school for free blacks and slaves to expose them to the Bible and hymns but teaching reading and writing wasn't part of it. Such schools were not uncommon in the south at the time and had they interfered with the property of the church members then such schools would have been brought to a rapid halt.
Even though the schools were legal there were plenty who were opposed to the idea of even Bible study for blacks and Jackson was quite steadfast in his support for the school.
Jackson historian Michael Aubrecht states: “ It wasn’t legal in Virginia at that time to teach slaves to read and write, but Jackson defied that directive. In order to conduct bible studies he had to do so.”