The autopsy concluded that the powder came from a fire extinguisher found beside Deby's body and that the head wound he had suffered was not the cause of his death.
Brahim, 27, was seen as his father's choice of successor, but was widely disliked even by some of his own family who viewed him as unfit to govern, causing a split within the ruling clan.
The president sacked Brahim as his adviser in June 2006 after he was arrested in a Paris discotheque for possessing an illegal firearm and drugs.
He was given a six-month suspended sentence by a French court.
A coalition of rebel forces have been fighting a war against President Deby's forces in eastern Chad, saying he was fraudulently elected. The rebels are demanding free, democratic elections to end his clan-based rule.
Makaila Nguebla, a Dakar-based spokesman for the Union of Forces for Democracy and Development (UFDD), said Brahim had been a key source of resentment who drove members of the president's administration to turn against him.
Nguebla said: "He is at the root of all the frustration. He used to slap government ministers, senior Chadian officials were humiliated by Deby's son."
"They had to leave the regime, go into the bush. They chose the military option instead of being humiliated inside Chad."
Nguebla said he believed Brahim's death would be a serious blow to his father's morale, particularly after one of his close nephews, the chief of Chad's armed forces, was killed in a clash with fighters last year.