In my opinion, the tattoos have different Art Styles that kinda reflect different culture.
Jinx has a combimation of clouds and bullets, which show that she is kind of a lunatic that loves shooting down everything till the last bullet (the video which has the image you posted also shows her relaxing in bathtub full of bullets). It is important to note that when you overuse a machine gun, it sometimes leaves a trail of smoke. Or it may reference the smoke created by her destruction or even Fishbones' explosive attacks. She most probably got the tatto for fun alongside her tons of belts and that weird bra. Her Pool Party leak reveal her tattoos more clearly:
https://i.imgur.com/EIYh2EB.jpg
Akali instead seems to have dragons and clouds, showing that she wants to reach high goals, dragons being generally a respectable symbol in eastern cultures. Some people theorize she is some kind of Yakuza Assassin. I think she made the tatto around the time she left Kinkou to express her freedom. And I feel it has some kind of ancient art style in it, while Jinx has some kind of smooth graffiti-like look? Idk.
https://www.artstation.com/artwork/d2vQ1
While it would be interesting to see an unlikely interaction, I think they are simply two tattooed characters and that is a coincidence that they have one element in common (clouds).