Two things cast doubt on that theory of mine:
1.This plant-name is more often (and more correctly) written 'Jacquinia'.
2.Jacquin(i)a looks a LOT like 'Jacquin', which is the name of a famous botanist (the Dutch born Austrian Baron Nikolaus Joseph
von Jacquin (1727-1817), who was professor of botany and chemistry at the University of Vienna). Needless to say this is a more probable origin of the plant-name than some unknown word from a native language.
On the plus side, I'm fairly sure I now know the origin of Jacquina: it is like the French name Jacquine, which means the same as Jacqueline
. The 'a' at the end is just a bit of Spanish influence.