I am assuming you had a typo and mean NvChad (edit: just now realized you did mention NvChad in the title already). Yes you can, but calling flatpak applications on the command line is kinda weird so I would actually suggest an alias if you want to be able to just type nvim in your terminal.
To start the flatpak version of neovim via the CLI you’ll need to type flatpak run io.neovim.nvim. Of course you don’t want to do that, so you can tell your terminal to remember that whenever you type nvim you actually meant flatpak run io.neovim.nvim. To do that you can put the following in your terminal: alias nvim=‘flatpak run io.neovim.nvim’
As far as I understand, NvChad is a plugin for neovim. The command they provide for installing it just downloads the necessary files to the default config location for neovim, and starts neovim. however the flatpak version of neovim seems to be using a different location for it’s configuration. This blog post seems to say that the config location for flatpak neovim is ~/.var/app/io.neovim.nvim/config/nvim/, so you’ll probably have to move the files there for NvChad to work.