Mr Byrne said his brother's belongings, such as photos and items left over from his school days, were ruined - except for some set aside in a small suitcase.
"When someone is in a council property in a very vulnerable position, they can be erased off the face of the earth. There's nothing of Chris left," he said.
The 30-year-old described how he jumped into the skip by the side of a busy road to recover what he could, two days after learning of his brother's death.
"It was absolutely crushing because Chris had such a personality," said Simon. "He had lots and lots of interests.
"He was such a nice guy."
Mr Byrne said the council did not contact him after Chris died. Instead, he said he was told by Chris's former foster parent, who had been contacted when the flat was cleared.
He said he complained to the local authority, but BHCC had not directly apologised to him for what happened, adding that he wanted basic recognition of what he called its mistake.
"Truth is, you cannot change the past, but you can have people try to avoid it happening again in the future," Simon said.
BHCC said in a statement: "During the process of cleaning the property and making it suitable for the next of kin to visit, some items were unfortunately disposed of by our cleaning contractor.
"We do understand how important someone’s belongings are to their friends and family and apologise for any additional distress and upset this caused in relation to this very sad loss."
It said it no longer used the company involved in the clearing of Chris's flat and it was "confident our current contractors share our expectation that people’s belongings are handled in a sensitive way and, where appropriate, passed to the next of kin".