Is it making the 2-3 shift? I mean does it go into 3rd?
If you are getting normal 1-2 shifts, but no 2-3 shift, you may have a sticking governor. There should be a cover on the side of the trans you can take off & remove the governor, As you lift the weights on the gov. the spool valve should move freely through its entire travel & return when you let it go, If it's sticking, try cleaning it with brake cleaner. I assume you have checked the modulator & it's vacuum line & adjusted the kick-down cable, if not you should, the three items work together.
PS On the cable where it attaches at the bracket by the carb, there is a piece that will release the cable, It is a plastic piece that you can either push up with your finger, or pry it up with a screwdriver, When you release the cable it will be tighter, then have someone depress the gas pedal to the floor and push that piece back down to lock the cable, some people try doing this by themselves by opening the throttle at the carb, the problem with that procedure is often the carb can actually open further than the pedal will open it, this results in a loose cable and the kick down does not work properly.