I received the kit for a trade in. Can I deliver the device in a Apple Store'?

You best check about that with Apple; we are all just other users here. They usually do not accept computers at the store and if you look at the shipping label, it should show a third party company it is going to. By the way, it is best to take pics of your device before packing it and make sure to copy the tracking number so you can check on it while in transit.

Yes, you can trade it in at an Apple store. I have done that a couple of times.

https://www.apple.com/shop/trade-in

Interesting; the last time I checked, the only devices for in-store trade in were iOS devices. It's great if you can now take in your Mac and do it there. Just out of curiosity, I just started the process online offering my iMac and this is where I stopped - it notes that the Mac will be sent in; no offer or taking it to the store:

The website that I posted above doesn’t state specifically that Macs can’t be traded in at the store, but I didn’t drill down like you did. And to clarify, I have traded in phones and iPads at the store.

I’m not sure what the OP wants to trade in either since it wasn’t mentioned.