Hey Kenneth,
the Onefinity CNC Controller user interface is a web page. You access it from the installed chromium browser on the HDMI monitor. You can of course open a new browser tab and navigate to any host that is accessible from your Onefinity Controller, and then download files. You will then have to move them to /var/lib/bbctrl/upload as root, then they will be found by the Controller and show up as g-code files in the Onefinity User Interface.
For this, the Onefinity Controller should have its network configured in /etc/network to a IP address in the private network range in order to be able to access the local net and the internet via your router. The automatic link-local (zeroconf) configuration with http://onefinity.local does not allow this.
Of course there are other services that are installed or could be installed on the Onefinity Controller. ssh is installed so you can transfer files in any direction with scp. See here for an example.
You may also install samba and smbmount and access SMB (windoze) shares.
You can also access the Onefinity CNC Controller user interface from any remote computer that is connected via the ethernet port or WiFi. In this case, you have access to the internet, can download files from the internet and upload them to the Onefinity controller the same way you would upload them from a USB stick if you were on the HDMI monitor.