The practical answer to this is more complicated than copyright and trademark, as WotC has specific rules that deal with this.
The short answer is that, you cannot use Kenku in your book. However, there are certain circumstances where you could:
If it's fan work that meets WotC's Fan Content Policy
If you don't actually mean "Kenku", but a dissimilar bird person that communicates with mimicry (still iffy, as they may decide it's too similar and sue you anyway)
Or you make your book in the Forgotten Realms and get hired by WotC
First, are you going to sell the book? If not, as long as you follow WotC's Fan Content Policy, you can use it. Free as defined thus:
You can use Wizards’ IP (except for the restrictions listed in #3) to make Fan Content that you share with the community for free. Free means FREE:
You can’t require payments, surveys, downloads, subscriptions, or email registration to access your Fan Content;
You can’t sell or license your Fan Content to any third parties for any type of compensation; and
Your Fan Content must be free for others (including Wizards) to view, access, share, and use without paying you anything, obtaining your approval, or giving you credit.
Let's say you do want to sell it, though. You're still not out of luck.
If make a raven-inspired bird person that talks by mimicry, stuck in a human body (you keep saying Kenku, but that's seems to be the most important aspect - incorporating something that real life birds can already do). And when this person does return to bird person form - simply give them functional wings and literally never call them Kenku.
It may talk like a "duck", but it will no longer look like one. Just as the Tengu of Pathfinder are wingless, but do not use mimicry (they look like a duck, but no longer talk like one), which distinguishes them from the version of Kenku they are based on (Third Edition Dungeons and Dragons, not Fifth, which is the version of Kenku you're interested in). In Legends of the Five Rings, Kenku diverge even further - they have huge wings and do not use mimicry. Additionally, it's pretty likely that if your character has limited mimicry to the point of being noticeably bad at human speech, you're going more by common ideas than what's implied or written about the Kenku's speech capabilities.
That could still be iffy if WotC decides that speech mimicry and being a raven person (regardless of wings) together are iconic enough to be a Kenku. So the more you focus on the core concept of speech mimicry and the more you diverge from Kenku as WotC presents them, the better off you'll be. Ravens are not the only birds that can mimic speech, for that matter. And the way Kenku mimic speak is fairly specific and limited. If their speech was more like an actual bird in sound (not a perfect reproduction of what they heard) that would diverge a bit. As would allowing the character to eventually reach fluency. Alternately, having the character learn sign-language (just don't make it Drow sign language, I guess?) might be another divergence.
However, if you literally want to sell books with a WotC Kenku character, specifically the Fifth Edition Kenku? You would need to get hired by WotC to write this book. From my understanding, Kenku, being from Volo's Guide to Monsters are not covered as Open Gaming License content. And since you'd be removing the Kenku from any Dungeons and Dragons setting, it's unlikely WotC would want to hire you. If you wanted to use Kenku exactly as they are, you should probably just set your book in the Forgotten Realm and try to sell it to them, because you'd be reproducing what WotC calls their "Product Identity".
For a more information (not all of it good) on WotC's practices in regards to this, see:
To what extent can a person use Wizards of the Coast's D&D monster information?
Are Drow Copyrighted? And OGL?