Technically, yes.
The official way for a kobold to be able to cast magic missile is for them to be a Kobold Scale Sorcerer (VGtM 167). These kobolds come in at CR 1, and are 3rd level spellcasters. While their published spell list doesn't have magic missile on it, the DM is well within their rights to change one of them (probably chromatic orb) to magic missile. If these kobolds became sorcerers, they could learn to cast the spell.
Your interpretation is flawed, though.
First, your source is bad. Googling "loredrake kobold" leads me to the D&D wiki, whose page has a big "Homebrew Page" banner on it. D&D wiki is a bad source for many reasons, one of which is that its homebrew is totally untested and unsupported. Thus, your source isn't saying that the rules allow kobolds to cast magic missile. Instead, it's saying some random person on the internet allows their kobolds to cast magic missile. Additionally, it looks like this page is designed for a player character that wants to play a kobold, not for kobolds as monsters. Finally, it looks like loredrake is a specific subtype of kobold, which means that if a kobold does not start as a loredrake, then they cannot become one. Again, this is homebrew, so it's hard to say.
Anything is technically "allowed"
Because the DM is the DM, they control the game--if they decide that some kobolds exist that can learn magic missile, then that's true for your game, because DMs have final say over monsters and rulings and the like. Therefore, "allowed" is a weird term to use in this scenario: different DMs can decide what they are willing to allow in their game.
I would suggest that you talk to your DM about your plan to teach them magic missile. It's certainly possible that they will agree--I've let my players train NPCs in class levels, and I've given them command over armies too. However, I've only done so under specific circumstances and with specific restrictions. Ultimately, it boils down to the type of game you're playing, and what the DM has in mind.
Finally, I'd advise you to be a little cautious. If my players enslaved 20 kobolds and taught them a powerful spell that required no material components, they might have to worry about ending up on the receiving end of all of those magic missiles...