Interesting claims, let's see how they hold up with established lore. Additionally, let's check personalities for compatibility. We don't want a ship to sink because it tears itself apart.
both love to kill
Jinx doesn't love to kill, she loves chaos and havoc. To paraphrase a rioter from a jinx AMA, If someone was standing in an alley, she wouldn't kill him just because. But if he were sitting on a crate of fireworks, she wouldn't think twice about setting them off.
Jhin, however, is an established compulsive killer. His "art" demands it. Not sure if he loves it though, some of his quotes hint that he hates what he has become.
both somehow love art
Not really sure we are ever shown that Jinx loves art, but she might.
Jhin, of course, call his killings art, so we can pass him on this.
They are both ADC, and were designed by the same designer
their names begins with J and are four letters long
Straight facts. Only Jhin has the four compulsion, but I imagine dating anyone with a different number of letters would be difficult for him.
They both gave names to their weapon(s)
Almost all weapons (guns especially) in league are named. It adds just that much to a character's personality. Just a fun fact.
Analysis:
Yes, they're both "crazy," but in completely different ways. I feel like Jinx is more akin to a kid who just wants to get out and flout authority and have fun. Her style of fun, however, involves destruction and explosions. She has some sort of split personality or personality projecting disorder, since she applies different personalities to her guns. However, she is arguably fully rational in her decision-making process, although she does not care about the general rules of society, considering them boring.
Jhin is completely unable to alter his behavior, having several compulsions and an exceedingly split personality between the stage worker and the artist. He is more methodical and controlled in setting up his work. His VO includes several lines about wanting to stop, but being unable to, showing that he cannot control his behavior.
Conclusion:
Based on the inherent difference between Jinx's chaotic and Jhin's controlled nature, I do not think these two would pair successfully. There is very little shared ground or interests for them to connect over. They do not find joy in the same things, although Jinx might find some of Jhin's magic bullets to have interesting effects for her own brand of excitement. Imagine how hard it would be for a sniper to appreciate a hyper kid in a candy store and you can see what I'm trying to get at.
I hereby give this ship a 1/5, would definitely sink.
Please note, this is from a character's personality and lore perspective. I completely understand some people do not care if ships make sense, but I feel if you are going to pair up some fictional characters, at least put them in a decent relationship.