The "gasket" (more like a circular rubber seal) that goes on the accelerator pump is available separately, but every kit I've used has come with a complete new accelerator pump assembly with a new seal and the spiral spring to keep it in place. I believe the newer seals are blue color to distinguish them from the stock black rubber seal.
Another item to check is the operation of the choke pull-off. It is controlled by engine vacuum and if the throttle is off the high idle cam (which allows the linkage to move freely) it will pull the choke away from full closed position in about 3-5 seconds whenever vacuum is applied. Its purpose is to let the choke be full rich to get the engine started, but then allow a little more air in once its running. If this is not working properly the engine may not run right after startup until the choke is fully opened by the spring mechanism.
The point of my explanation of the choke pulloff is that the choke has to be adjusted so that you get a very rich choke position for starting, and then normal choke operation for further warmup (it then moves based on spring in the choke housing). The rebuilder should have checked to make sure this mechanism is there and it works.
The way my carb works when cold is I pump it 2-3 times to get fuel into the carb, and then turn the key with my foot off the accelerator and it will fire up. Since it is cold and the choke is on, the throttle is on the high idle cam and the choke is almost completely closed. I just let it run in this rich position for about a minute, and then raise engine speed a little to let the choke pulloff move the choke plate farther open for further warmup. If the weather is colder (teens, etc.) I might have to let it run longer in the rich position, sometimes for several minutes.
Bruce