It is not clear what you are doing.
You need to run Tiny Core from the CD.
Connect to the internet.
Install dosfstools and syslinux. (If you will select Zip, you also need to install per15.)
Run USB Installation.
Selecting Ext is ideal for most people.
After installation is complete, boot from the USB drive (if it won't boot, you may need to change BIOS settings.)
When running from the USB drive, connect to the internet and install programs you want on the USB drive.
If you can't do it this way, for some reason, there are other ways.