Hey everybody, here's my theory on the origin & mechanics of Amon's bending-theft:
Amon, being an amazing waterbending prodigy, used a corrupted form of water-healing to disrupt the flow of chi in his victims' bodies. This disruption caused one, some, or all of his victims' chakras to lock, which sealed off their bending and made healing them impossible for anyone but an energybender.
Because Amon was a waterbending prodigy it's reasonable to assume he attempted to learn every bending art associated with his element, which means he would have learned water-healing. To understand why that's important I have to tell you this: water-healing is the act of manipulating the chi in another person's body by using water as a catalyst. This means water-healing is actually a form of energybending, allbeit very specialized and limited. Because Amon was capable of bloodbending this means he likely could have performed a form of water-healing without using external water. But how would he know what to do?
Here's how: early in LoK Amon demonstrates that he's also a master chi-blocker. Because of what chi-blocking does it's a good bet that part of chi-blocking training is learning how chi moves through the body. This would have given Amon special insight into chi-manipulation, something very few benders seem to have.
Finally, we have the chakras. Chakra-opening is not a bending art at all, and can be learned by anyone. It's not impossible that Amon found his very own guru to teach him how to open his chakras, the same way Guru Pathik taught Aang in TLA. From Guru Pathik's teachings in TLA we learn that a locked chakra can block the flow of chi throughout the body, hindering the body's performance. We also learn that when one of Aang's chakras locked he lost access to the avatar state, and the only thing that could unlock Aang's locked chakra was the timely intervention of an energybending lion-turtle.
So let's put this all together, the way Amon might have. Amon is a person with the exceptionally rare ability to manipulate other peoples' blood. He's also a person with master-grade knowledge of how chi moves throughout the body. Add to that his presumed knowledges of internal chi-manipulation (through water-healing) and chakra manipulation (through spiritual learning) and a likely explanation of his bending-theft appears.
Amon used his bloodbending to perform a strange version of water-healing on his victims. However, unlike normal water healers who improve the flow of chi, Amon intentionally disrupted the chi in his victims' bodies. This trauma caused one, some, or all of his victims' chakras to lock, sealing off their bending in a way that couldn't be healed by anyone but an energybender avatar.