The major connection between these two is that in both cases there was tension between poor whites and rich whites even as both white groups were willing to abuse and exploit Indians.
In both cases, the poor whites were not happy with the way that the elites were behaving. Bacon's Rebellion was largely about class. Zinn portrays common soldiers as being unhappy with Jackson's wars against the Indians.
However, in both cases, both poor and rich whites were happy to abuse the Indians. Bacon's rebels killed friendly Indians. Jackson used friendly Indians to defeat hostile Indians, only to betray them later.
In these ways, there are similarities between the two.