Exhaust duct

I recently moved into a home and it appears that the backside of our exhaust for the furnace and water heater is pretty much gone. Id like to replace this myself, being the handy sorta guy I am lol, but I'm also not trying to continue to poison my children with co2. So what are the ways to resolve this ladies and gents? I'm happy to get whatever sorta patching/caulking necessary for the brick, unless that's not necesarry. i just wanna donecessary. First photo is the backside and the last 2 are the setup to it, just to clarify.