Hi Kevin and welcome to Support Forum. No worries, I will help you to run AmiKit X on your computer (especially if AmiKit 8 runs on the same config).
First, let me know what PC config you have including the Windows version.
How does the never-disappearing WinUAE window looks like? Can you send a screenshot?
Does it help if you update WinUAE to the latest version? It's simple, just copy the newest winuae.exe there as described here: http://bit.ly/2G2KyRS
Did you install kick.rom using RomFind.exe? If not, please do so and make sure it found A1200 ROM file.
Jan (AmiKit Designer)