I've played in and run evil campaigns of various sorts in both 3.5 and 4e (though not 5e, I think my learning will transfer), and run into a lot of problems: My Guy Syndrome comes up a lot, as does a tendency to default to a regular D&D storyline only with more stealing of spoons and kicking of puppies to remind ourselves we're evil. Sometimes an evil campaign instead descends into over-the-top motiveless violence until there's no story at all. There's a whole host of at-the-table and in-the-story issues, and I tried many different strategies to address them. Eventually I came up with a framing device which works well for us in avoiding these problems:

Provide the PCs with a Master to guide them toward orchestrated works of Evil.

Start the game with the PCs as underlings/minions/hirelings/apprentices/etc of a powerful evil NPC. The Master has a complicated Evil Plan and he tasks his minions to enact various parts as the Plan progresses: "Bring me the soul of a hound archon," "Raze the border keep," "Steal the Apocalypse Gem," "Help a spy infiltrate the paladin's ranks," and so forth, tailored to the PCs' abilities.

This provides the party a reason to work together despite having different agendas (and working together will hopefully bond them as friends so that they want to continue as a group) and establishes small achievable evil goals that accumulate into an Epic Evil Event.

All you need to do is ask the players to make sure their characters have a good reason to work for the Master: The serial killer likes having his rampages subsidised (and the Master protects him from the Law); the necromancer seeks to learn from the Master's experience and gain access to his libraries of forbidden lore; the mercenary's in it for the money and benefits.

Eventually the Apprentices will surpass their Master.

Expect the party to betray their Master at some point, hijacking his Evil Plot for their own gain: this is not only expected, but awesome. It's the Master's Evil Plot, not yours, and the story isn't about the Master--it's about his apprentices. Consider the Master to be training wheels for evil, setting an example which the party can then follow to surpass and overthrow their instructor as they level up.

This works because Evil Needs Goals.

As Ed describes so well and AgentPaper elaborates in the D&D context, evil needs concrete reasons motivating its actions. The Master provides goals and motives while the players find their feet in the new paradigm, channeling and guiding their exploration of what it means to be evil in ways compatible with the D&D paradigm without simply kicking puppies during a dungeoncrawl.

A word of warning: Alignment is tricky.

D&D has a history of the details and nature of alignment sparking major heartfelt arguments, because D&D alignments are not easily (or appropriately) matched to real-world philosophies and moralities; they're narrative simplifications to support the game's conceits and draw their power from storytelling conventions rather than from genuine moral complexity. Exactly what this means and how to deal with it are beyond the scope of this answer (and possibly this site, although there's a LOT of questions on the topic you can look at), but you should be aware it exists and be ready to talk with your players about what "Evil campaign" means to them so there aren't nasty surprises mid-game.

It's called Armor.

What do the Rules say? I think the applicable rules are armor rules. The intent behind wrapping chains around yourselves is protect yourselves. That is the job of armor.

Chain fashioned around your self are similar (enough) to Chain mail or ring mail, both are heavy armor. Chain mail requires strength of 13 and imposing disadvantage to stealth. For that you get an AC of 16. Those chains have no HP, and no mechanism for it to be destroyed for simplification reasons.

Adding other objects to the character to act as armor isn't necessarily outside the rules, but isn't something the rules consider. Which means that what happens is left up to the DM. The most appropriate rules for this sort of thing are the armor rules, not the object HP rules. Adding armor in this fashion should affect AC, not add additional HP, and depending on the amount of chain likely have stealth implications.

Object Rules

The barrel is what item HP are meant for, a situations that happens to come up where someone needs to destroy an object. The rules on objects are for objects, not armor. The rules for objects can be found in the SRD ( official ) in Game Mechanics under Objects. Reading them it is clear that the intent is an item caught in the cross fire, or the characters try to destroy an object. It isn't meant for items that are worn to provide temporary hit points.

This path might inspire your DM to employ armor/weapon damage house rules. Your swords might suddenly break or shields shatter. That is the logical extension of applying these HP rules to all things in the world.

Ultimately, it's the DM's Call

To apply armor rules or object rules is the DMs choice. Armor rules are the ones intended for defense, but there is nothing preventing him from applying object rules the way he has already.