Zsh users at times need to use a bash completion script. This is necessitated by Developers who only write bash completion scripts for their tools. On the bright side, zsh has a bash completion script compatibility mode, you have to enable it before loading a bash completion script inside .zshrc.
Add below lines to your ~/.zshrc file before the source line.
autoload bashcompinit bashcompinit
You can also add the lines on top of the zshrc file to make sure no bash script is sourced prior to its loading.
These are the lines in my ~/.zshrc to enable bash completion for Cheat.
autoload bashcompinit bashcompinit source /etc/profile.d/cheat.bash
I tested and confirmed to be working.
$ cheat <TAB> zsh: do you wish to see all 1254 possibilities (1254 lines)?
Let me know if it worked for your environment. Also check