Had a discussion recently in my household about whether you can do this.
I had an older insinkerator in my previous place which I threw everything into it (apart from banana skins and really hard and fibrous stuff.)
I figured some leftover cooked chicken bones was fine as I would do this all the time in the past.
Discussion and debate ensued. Google search result vs google search result.
Wigglywisdom.com says its forbidden (one of the top search results). I found the insinkerator website says that cooked poultry bones are fine. But I was still not satisfied.
So I emailed Insinkerator. They said: "Would not recommend chicken bones unless you have 0.75 hp or better insinkerator."
Advised that they might want to add that detail to their FAQ.
Looked up the model of my previous insinkerator and it was the 65, meaning it was 0.75 hp.