I've finally worked out a fairly reliable way to load videos onto my sons kindle fire kids profile so he can watch them offline :) Netflix / Disney plus works but we have some family videos he likes to watch.

• Enter the Adult profile of the Kindle Fire. Make sure WiFi is turned on.
• In the Amazon App Store, download ES File Explorer and VLC media Player.
• Still in the adult profile, run Freetime, click the settings / gear icon beside the child profile
• Click add content, choose ES File Explorer and VLC
• Go to the Child Profile
• Run ES File Explorer, give it a minute the first time as it appears to download it again. Go through the ES options but don't do premium, click the cross near the top right.
• On the left, click Network, view on PC. Note that URL it gives, which will be something like ftp://192.168.1.50:1234
• Install FileZille on your PC, or run another FTP Client. Connect using the details provided in ES File Explorer, the screenshot below. The key settings are Protocol: FTP, Host is 192.x.x.x that ES file explorer gave you, encryption is "only use plain FTP (Insecure)", Login type is "anonymous". You then click ok.
• In your FTP program navigate to the Movies folder. Create subfolders if you like. Upload files using your FTP Client. It can take a while to upload,
• Start VLC, click settings (more -> settings). Click "Media Library folders". Click "Internal Memory" (but leave it unticked). Tick the box beside Movies.
• Reboot your Kindle (might not be necessary, I found it useful to get VLC to pick up the videos)