Linux – Can Kali installed from Kali 64-bit iso run on 32-bit platform

Not possible. You will probably get the following error message(or some message that is similar to this one):

If you have 32bit machines, it is safer to download a 32bit OS to boot on both architecture options.

Note also that when talking about EFI, there are some machines that have 32bit EFI, but run amd64 processor so, there are some tweaks that need to be made to make this kind of "boot freak machines" work. Take a look at the related stuff section of this answer.

There is also this question on AskUbuntu where you can find interesting stuff about dual booting Ubuntu 32-bit EFI and 64-bit EFI. Since Kali Linux is based on Debian, some of the tips could apply to your scenario. As said in the comments, this setup should be possible if using a 32-bit EFI to chainload both kernels, and isolating the / on 2 different partitions, making 2 different installations on the same disk.

It should be possible to share swap partitions although you could break your system if you "suspend to disk" and then boot on another of your Linux installs. The same way you could share your /home partition but you could break software that use files that are architecture dependent like rrd database files, getting the ERROR: This RRD was created on another architecture error.

Related Stuff:

• Installing Windows x64 on 32-bit UEFI (EFI-IA32) via GRUB [duplicate]
• How do I repair grub2 (not) booting 32-bit EFI on a 64-bit machine?
• Arch Linux Wiki: Booting 64-bit kernel on 32-bit UEFI

My opinion: If you really want an OS that will be able to boot on i686 and amd64 i suggest you to use an i686 Linux distribution.