One of the Cloanto's updates to Amiga Forever 8 includes SetPatch 44.43 which, unfortunately, prevents Screenmode Prefs program from launching at the end of AmiKit installation process. This results in an endless loop of AmiKit asking you to set a screen mode while the Screenmode Prefs program never appears.
If you're experiencing this particular problem, simply re-download Amiga Forever installer and/or ISO as this was fixed in newer releases.
You can install AmiKit even without updating Amiga Forever, though. Here's how:
1) When you end up in the loop described above, quit the emulation.
2) Run AmiKit.exe launcher and click Configure button. A WinUAE window will appear.
3) Go to "ROM" section and click "..." button in upper right corner to select a new ROM file. Select the ROM named "amiga-os-3x0-a1200.rom" usually located in "Amiga Files\Shared\rom" folder of your Amiga Forever ISO, or if you installed Amiga Forever on your Windows, you should find it in "C:\Users\Public\Documents\Amiga Files\Shared\rom" folder.
(Just make sure you selected the ROM with 3x0 in its name and not 310. Also Do NOT save the new settings.)
4) Just click the "Start" button and finish the AmiKit installation by selecting your preferred screen mode - the Screenmode Prefs program should appear now.
5) Once it's done and AmiKit says "Installation Complete", quit the emulation and restart it - simply run AmiKit.exe launcher and click the "Launch button".
I am sorry for the inconvenience.