How do I replace a mechanical plumbing vent for the kitchen sink?

you can build a loop system or buy a mechanical vent try cleanning the drain line first

Augers and Plungers
“Drain Bladder, Cobra Products”
__________________________________________________________________________

“Craft@Hrs”,”Unit”,”Material”,”Labor”,”Total”
__________________________________________________________________________

“Drain Bladder, Cobra Products”
“Attaches to any garden hose. All brass fittings. Quality rubber construction. Environmentally safe.”
__________________________________________________________________________

SKU 357945, Medium, 1-1/2″ to 3″–10.98

SKU 359386, Large, 4″ to 6″–16.98

__________________________________________________________________________

“”

This item can be inserted in the vent pipe coming out of your roof. Make sure you get it past the T in the wall where your kit sink drain attaches. Have someone ensure your sink does not overflow with water. Turn the hose on and the pressure will probably remove the clog. Ask your home depot for more info if you need it.