No its not the kickdown adjustment--that is a band adjustment. The throttle pressure is control by the throttle-duh, in stock form its rod from the carb to the trans. It can be adjusted by bending the rod or by the trans.
It sounds like you should take the car to a shop but sadly not all shops are fair and honest.
You could try to give it some more throttle pressure. I can't post any pictures cause I went to a manual valve body and could throw the rod away.
You want to watch the rod move as you open the throttle and then adjust it so it doesn't come back in all the way when the throttle is closed and moves deeper in...there is a limit since too much will not allow the throttle to open fully. But if you can open the throttle all the way and still can move the rod deeper in, then its set wrong. What you like is the rod all the way in at full throttle. When the trans is slipping from age you might want it all the way in at 80 to 90% full throttle
