I understand your wanting to vent the appliance to the shared flue, and I'm not the saftey police. But in my profession I see all kinds of things done wrong, it's what I am paid to look for.
The basics with gas are you need to give it enough pipe to vent correctly. Water is a by-product of gas , and rots pipes and chimney flues.
Fit to many together at the wrong connection points and you will have Carbon monoxide leaks and improperly working units down the line. They will also damage your clay flue liners in your brick chimney if that is what it is venting into.
So basically you save a buck now, and it will cost you down the line. It can also cost serious harm to your family.
Just my opinion, but my family is worth way more than a couple pieces of pipe and some extra money.
As always, get a CO detector, with any combustion units.
I'm just trying to help and be firm in my opinion.