Good for your player -- he's recruited some temporary NPCs to help the group out!
Your header question asks how to "balance" this, but there's not a need for balance considerations since these NPCs are temporary. Your player will need to keep making checks to keep the guard drakes on his side.
You should have the guard drakes act on your rogue player's turn, for simplicity. You might assign your rogue player to run the guard drakes, or you might run them yourself to emphasize to the group that the guard drakes are temporary allies who make decisions for themselves and don't blindly obey.
At the start of each battle, your player might need to make an Animal Handling check to convince the guard drakes to attack. If the opponent is something the guard drakes would naturally want to attack, the check might be very easy, or no check might be required; if the opponent is something the guard drakes consider an ally, the check might be very difficult, and failure would likely mean the guard drakes attack your player.
Unfortunately for your player, most of the creatures in this area are creatures the guard drakes might consider to be allies. Kobolds are tending to the dragon eggs in this area, and the guard drakes know that the kobolds are their allies. Cultists are humans, but they're members of a dragon cult and they speak draconic, so the guard drakes probably won't attack those without some persuasion. The guard drakes might be willing to attack some of the human guards and berserkers in the area, though.
For the long term, it's probably best if you rule that the guard drakes won't leave this cave. Their job is to guard those dragon eggs, after all. And they're going to want to sleep in their nest, not on a bunch of dirt in the forest. This will ensure that the guard drakes don't somehow become permanent allies of the group.