It seems I can't get them:
tc@box:~$ tce-load -wi linux-`uname -r`_api_headers
Downloading: linux-4.14.10-tinycore_api_headers.tcz
Connecting to repo.tinycorelinux.net (89.22.99.37:80)
wget: server returned error: HTTP/1.1 404 Not Found
md5sum: linux-4.14.10-tinycore_api_headers.tcz.md5.txt: No such file or directory
Error on linux-4.14.10-tinycore_api_headers.tcz
tc@box:~$
I also tried linux-4.14.10_api_headers.tcz. The App-tool offers headers for 4.14.3, but that doesn't look right, or?