Pi Zero you mean the original Pi Zero 1 right? Its SoC is driving a 32-bit ARMv6 CPU core.
The most straightfoward way is to try the Cloudflare Package Repository. It should be able to match the OS and arch for you.
You can also try installing the precompiled ARM deb package, specifically cloudflared-linux-arm.deb
directly if the repo does not work.
P.S. If none of the above works, you can try setting up the Go build environment and compiling from source on your Pi Zero.