Why did they burn?
Rashi citing Targum Yonasan: They burned for them like they burn for kings there. We burn for kings; this is not Darchei ha'Emori (following Nochri superstitions - Avodah Zarah 11a).
What did they burn?
Radak citing Avodah Zarah 11a: They burned their beds and the Kelim that they used.
Radak #1, Malbim: Perhaps they embalmed them via sharp spices that burn the body, like (Bereishis 50:2) "va'Yachantu ha'Rof'im." 1
Radak #2: Perhaps they burned the flesh. It had become wormy, and they did not want to bury them with the worms, for it is not honorable. They burned the flesh and buried the bones.
This is unlike the opinion that Yosef was punished for embalming his father (refer to Bereishis 50:25:151:3).
