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Get a level II inspection of the chimney first. Look at all the spalling near the top. A lot of freeze-thaw damage on that cold exterior chimney. Reline it with a properly sized smooth wall 316Ti or 316L ss liner. Sweep the liner into the Combustion Appliance Zone and cement in place. Once in the room, split it to the DHW and boiler, which btw appears to be running downhill. If you sweep it into the room, as allowed under the IRC Ch24, you don't need a clean out for gas.

According to Ch15 of the IRC, the max length of a Flexible Transition Duct or 'Slinky' is 8 ft. it can only attach to the appliance and not start further along. It must be stretched until the inner lining is smooth to maintain the minimum cross-sectional area. No male down fittings such as that band clamp on the elbow. Any Slinky must be listed to UL 2158A. It is not approved for direct contact with those hot vent connectors.

You need to rework those vent connectors, min. 3 screws per joint equidistantly spaced, no seams from 5-7 O'clock pitched up towards the chimney 1/4" per LF. The larger connector must be heavier gauge pipe. I'd replace that crummy ground key gas cock on the WH.

Ask Hector the Inspector how he wants it terminated: as-is or extended with hard duct out from the building 3 feet supported.

I would skip all the flimsy material and just run a continuous 4" smooth wall 316ss chimney liner as your one-piece exhaust duct. It exceeds the code. Use a ss wall termination extended out from the bldg. 3 ft. with a strong steel hanger off that post and angled away from the wood.

Yes, that is a gas furnace vent cap. it is designed to keep rain from falling into the exhaust vent of a gas fired heating system of sorts.

This is not the first time something that was intended for one thing was used for another. I can give you an example of other devices used for things that they were not intended for. My biggest regret is when computers stopped including cup holders.

is there an eyeroll reaction?