What's the best way to clean/dispose contaminated lab equipment?

I have this flask full of E.coli that nobody has used for a while in the fridge and should be thrown out, but I want to double check that it’s okay to just put it in the autoclave to kill the cells and then clean the flask itself. The flask has terrific broth with chloramphenicol. What stopped me is the chloramphenicol. When I made this broth a long time ago, the procedure told me to make sure to add the chloramphenicol AFTER autoclaving the flask full of terrific broth, which makes me wonder if for some reason chloramphenicol shouldn’t be in the autoclave.

I also have a bunch of stuff in the autoclave trash I’m not quite sure how to dispose. It’s all in this special biohazard trash bag. It’s nothing serious, just E.coli and possibly some fungi that grew on petri dishes. But do I just wrap everything up in the biohazard trash bag and put it in the autoclave?