OK, once you manage to transfer AmiKit files from PC to Amiga, the automatic installation of AmigaOS files will probably not work on Amiga, but you can try it. Better idea is to install the AmigaOS files on PC and then transfer the files to "real" Amiga.
EDIT: The automatic installation of AmigaOS files on "real" Amiga is reported to work! You just need to modify the CD0 file (AmiKit:Prefs/Presets/AmiKit/Install/CD0) and replace the "uaescsi.device" string with the device where your CD is mounted (eg. scsi.device). Change the Unit number if necessary.
Once the AmiKit is fully installed, it contains the pack of pre-configured screenmode preferences and one of them is selected by the user during the installation. However, all of these screenmode preferences are set to use 32bit UAEgfx drivers which works under UAE only, of course. So whatever screenmode you choose it won't work for you on "real" Amiga. Therefore, before you boot the AmiKit, you should install YOUR gfx drivers and save YOUR OWN screenmode preferences using the AmiKit:Prefs/Screenmode program. Or you might want to copy your "real" Amiga screenmode prefs to AmiKit (ENVARC:Sys/Screenmode.prefs).
Edit the startup-sequence and disable the boot picture (SYS:Utilities/Expansion/ShowAmiga96/Bin/ShowAmiga96_Rev239C18 line). Otherwise, in case something crashes during the boot, you won't notice it because the crash message appears behind the picture. In addition boot pictures are also adjusted for UAE but I am not sure about this.
It is hard to tell you what all can be in conflict with classic Amiga. Eg. MMkeyboard started in WBStartup will report an error (it's UAE version). It is a good idea to disable WBStartup completely. Yes, the AHI drivers are UAE too.
Also, the AfA_OS might not work on your system, but this is rather rare. AfA_OS provide TrueType font support but try to disable it in startup-sequence for a while (it's C:AfA_OS_Loader line).
Also it might happen that IPrefs crashes during the boot (especially if AfA_OS is disabled). Therefore enable "C:Wait 1" line in front of C:IPrefs command in startup-sequence. Also enable this command in front of "Run >NIL: SYS:Utilities/Expansion/Birdie/Birdie ? <Env:Birdie.prefs" line. You might also want to increase the time to wait to eg. 2 or 3 (C:Wait 3) for testing purposes.
I would also disable the MakeLink commands in startup-sequence. They might be in conflict with your filesystem, who knows.
"C:PatchMSB" command must also be disabled as it calls special UAE math library. You should also copy your regular math libraries from your "real" Amiga to AmiKit:Libs.
Also enable "BindDrivers" command and disable "C:Picasso96fix" command.
In case of low of memory, decrease "C:StackAttack 32768" command to something like "C:StackAttack 8192". You might want to do the same in DOpus/Environmet preferences.
Next, Warp3D libraries are UAE versions. You can find the regular versions in Libs:bak drawer. Also watch out for P96 rtg.library as it's also UAE optimized.