In Doctor Strange, How did Kaecilius get set free after he was chained by Dr. Strange.
One of Kaecilius' acolytes comes and rescues him, and presumably frees him off screen.
Stephen: You think that's funny?
Kaecilius: No. No, Doctor. What's funny is that you've lost your sling ring.
At this, Strange realizes his ring is gone as a portal opens behind him, and he is shot with some sort of weapon. An acolyte comes up and pushes Strange down the stairs.
The next shot we see is of a wounded Strange hobbling down the hallway. Kaecilius is gone.
We don't know as it all happens off-screen.
It's possible he had other henchmen around and they released him.
A Wikia entry would seem to confirm this:
Strange removed the mouthpiece of the device [the Crimson Bands of Cyttorak] so he could understand what Kaecilius was saying. Soon after, Kaecilius' followers, the Zealots attack Strange, forcing him to retreat. The Zealots then destroyed the device, freeing Kaecilius.
Strange took The muffler off of Kaecilius before leaving making it easy for him to try and convince Mordo to despise the ancient one and let him free, after strange returns and realizes Kaecilius is gone Mordo is the first one to enter the scene. I think Mordo let him escape especially after his comment at the end of the movie to Strange.