Christopher Tolkien obviously researched his father's work in great thoroughness. Therefore, he obviously knew a great deal about the languages his father created.
But was he fluent in any of them? His father said that one of them (I forget which) was in some figurative, essential way, his "true native language", so I assume he was fluent in them, and could write at ease. But was Christopher the same way?
The languages Tolkien created simply were never developed to the point where they can support a modern conversation. Tolkien primarily used his constructed languages for poems, and he developed them as needed.
As the languages exist now, they are simply not complete enough for anyone to be "fluent" in, with many essential elements either not existing, or existing in many contradictory forms.
To quote a recent interview with Carl Hostetter, one of the editors of Tolkien's linguistic papers:
Can one simply learn tolkien's languages?
Carl Hostetter: If you mean learn in the sense of learn to speak, I would say a short answer is "no". Now the reason for that is there's a lot of points of grammar about which tolkien either wrote too little or too much - his language has changed across his life every bit as much as the legendarium did - perhaps more so. So for for example for a long time we didn't have a complete paradigm of the personal pronouns - in either Quenya or Sindarin. Well now we have a number of them to choose from. So if you really want to turn it into a spoken language you all have to agree on what system you're going to use. There's quite a bit of vocabulary, but given the nature of what tolkien was doing with the languages, a lot of them are more geared towards poetic concepts, certainly the natural world, but you're not going to find a lot of what we as english speakers consider to be working day vocabulary. So if you want to be able to hold a casual conversation about the nightly news you're going to have to invent a lot of stuff. And that's very hard to do on the fly. You can certainly learn a great a great deal about Tolkien's languages but in terms of learning to speak them, again I would have to say no unless it's highly qualified as if you get enough people together and they agree on a common set of grammar rules and vocabulary and can make up vocabulary. You could make a spoken language out of [or] based on tolkien's language, but it still would not be Tolkien's languages.
The Tolkien Road Podcast - 0251 - Interview with Carl Hostetter [31:59-34:07]
Christopher certainly knew a lot about his father's languages, probably almost on par with the people who are now editing and publishing those notes, but even knowing everything there is to know about an incomplete language will not be enough to achieve fluency.
