Does chametz that belonged to a Jew over Pesach need to be burnt afterwards or is it enough to throw it away…
It is sufficient to throw it away.
The entire concept of burning applies to chametz before Pesach (according to Rabbi Yehudah), and to a number of Torah mandated prohibitions.
It does not apply to this rabbinic prohibition.
See Shulchan Aruch 548:3 and Mishnah Berurah (where the idea of burning is not mentioned).