The short answer is "probably through the Messenger Kids app".
I've never installed this app, but its cousin "Messenger" stores all of its data privately, i.e. in /data/data/com.<whatever>, which is a location you won't be able to access via a file browser on an unrooted phone. This is normal: it's how one app keeps its data from being accessible to every other app on your phone (a basic security/privacy measure). And even if you could, I doubt that would be a good way of selectively cleaning stuff out: a lot of the content is probably in one or more databases rather than one file per message, so a file browser wouldn't be able to do much other than delete the whole lot.
So as I say, I don't have this app, but what you describe fits what I'd expect based on other Facebook apps. Hence I'd think the way to clean up would be to go into the Messenger Kids app itself and start deleting stuff from in there. You can use the app manager to clean the app's "cache" (temporary files, which can always be safely removedt), but apart from that or wiping the entire app you won't be able to do anything else from there.
Now whether this app has a friendly setting for deleting older content, or whether your only option is to delete either entire threads or individual messages I don't know (but that is basically all the full fat Messenger allows - not even "multi-select" for deleting groups of messages. It's almost like Facebook don't want you to remove things, and don't care about your storage use...).
From the amount of space it's using I assume that they've sent/received a lot of videos? I can't think of anything else that would use that much space.