FOR THE LOVE OF GOD !!! It's NOT a kickdown. OK, so you're a noob !!! We'll let you have a pass this time, but you will get educated.
Kickdown is a FORD term, and is usually a rod, not a cable. On a 700r4 it's called a TV cable as in Throttle Valve. In a Th350 it's a Detent Cable. Does similar to what a 700r4 cable does, but a 700r4 cable does more and is much more critical to be set right. It's use is to communicate with the transmission and tell how much throttle pressure you're giving the engine, whether it be light throttle, part throttle, half throttle, WOT as in Wide Open Throttle. YES, it does also control downshift aka passing gear. But the cable also helps determine shift points with the governor and vacuum modulator. Without that cable hooked up your shifts will be very early. If it's set to tight, you will shift late. In the 700r4 the cable setting also determines fluid pressure so it's critical on a 700r4 and will cook a transmission in no time if not set right. Good thing about a Th350, it doesn't regulate fluid pressure, so your Th350 will not be trashed if you don't have the cable hooked up.
You might have the wrong cable on that transmission. On some passenger cars, the cable goes back to the firewall and hooks to the gas pedal linkage. On our trucks it's supposed to be hooked to the carb or TBI linkage. So first things first, find the cable on the passenger side of your transmission and follow it and find the end of it and where it's going.