Hello @CSA Nathan ,
You need not install chectl tool inside the created kuberenetes cluster. This chectl CLI utility needs to be installed after you connect to the azure subscription that is running using AKS cluster.
This tool is just a client tool that can run from anywhere as documentation suggests it will read a valid config file for connection to a cluster so can be run from either Windows or Linux.
In case if you are using windows, run this below command directly on PowerShell
C:\Users> Set-ExecutionPolicy Bypass -Scope Process -Force; iex ((New-Object System.Net.WebClient).DownloadString('https://www.eclipse.org/che/chectl/win/'))
In case if you are using Linux Bash, follow the steps from here using-the-chectl-management-tool
Please "Accept as Answer" and Upvote if any of above helped so that, it can help others in community looking for remediation for the similar issues.