Cypress doesn't have any official tools for FOTA with complete automation. We still recommend our customers to use CySmart Android and windows tools. So we recommend you to use that software source code and develop the application according to your requirement.
Can you refer me to a document that describes the FOTA protocol?
For example, the actual bytes to be sent and received and via which characteristics etc.
I don't know if this will help but here is a link to a Cypress webpage that claims to have the CySmart source code.
If you're adventurous, you can modify it to your needs. If not, it may have commented sections to describe the FOTA protocol.