install into ESP to boot via UEFI

[core-user]

You should be looking in here.
http://www.tinycorelinux.net/6.x/x86_64/release/distribution_files/

[Juanito]

Also, I already have bootable GNU/Linux kernel on this machine (as part of ubuntu installation). Can I reuse this to boot tinycore or there's some specific patches by TC which would prevent that from working?

As long as your existing installation is (u)efi boot, yes.

[suare]

You should be looking in here.
http://www.tinycorelinux.net/6.x/x86_64/release/distribution_files/

Thanks! It's kinda confusing that bigger TinyCP got EFI inside while smaller CP doesn't.

[Juanito]

The (u)efi files in TinyCorePure64 are only there so it can be (u)efi booted when burned to cd/dvd.

Since you already have a (u)efi installation, you only need to copy corepure64.gz and vmlinuz64 to a suitable location and add an additional menu item in your boot loader configuration file to get things working.