BotRK -> Zeal Item -> ?
I'd need a lot more time and words to go into it more, but that's basically the core items. Go Runaans if you're getting a lot of stacks, RFC if you need more safety, and Shiv if neither of those two fit. Get last whisper item as necessary and whatever defensive item you need. Just note that your most valued stats are armor penetration, attack speed, lifesteal, and stacks. I feel like playing her ADC is more viable now than when I spammed the shit out of it back in the preseason, since I'm noticing that I can have a lot of burst damage after only three items (BotRK+Runaans+Shiv) rather than only being able to 2-shot a Rengar after getting full build alongside all my stacks. It doesn't hurt that Fervor is a solid keystone now, since it synergizes with her kit better than thunderlords decree.
I wanted to test out getting Essence Reaver as my defensive item when I can rely on just my ultimate for defense just so the CD on it goes down (and CDR is close to useless on her otherwise), but I have yet to ever test it in game.
For abilities, you go W-Q-E-Q --- R>Q>E>W
Runes are standard ADC runes.
Masteries are either 18/12/0 or 18/0/12; you go the latter page for all the extra regen stuff if you're unsure about yourself and want to be safer in lane, but otherwise you go for the former since it's far better during the trades themselves. You can take thunderlords decree to make the early game easier to snowball, but fervor completely outscales it before too long.
You want to hit level 2 on her ASAP, but don't use W level 1 unless your lane opponents are aggressively trading. If you find an opportunity to trade level 2 (hopefully before they level up themselves), then take it. Kindred's level 2 is still very strong. Otherwise, just take opportunities to do an AA-Q-W-AA combo throughout laning phase whenever they're out of position enough to allow it. If you have a support that can all-in, then you definitely have enough damage early game to make it work. Make sure you're marking the right targets and that the support knows who is marked, though.
If the dragon crab gets marked, push up the lane and go grab it. If it shows up very fast, it'll take close to no effort to take if you go for it immediately. Otherwise, take opportunities to get them whenever possible, since the single best way you can snowball on Kindred is to get 6 stacks fast, take the rift herald for another stack, then take baron shortly afterwards for yet another stack. This is unrealistic unless your team specifically strategizes around it, but this should be what you're aiming for in most games.
One last tip: Kindred is a fantastic 1v1 duelist thanks to her ultimate. If you get low and use your ultimate and they're somewhat low as well, queue up your E up to two stacks and AA->Q the moment your ult ends. It almost always works if they aren't specifically playing around it.
Other than that, good luck. Her ultimate is NOT easy to use correctly in the slightest, and it's devastating to your team when you fail it. You have to understand the gamestate and have foresight as to what will happen in teamfights in order to use it well (and I'm still not the best at this either), so don't feel bad if she doesn't click for you right away. It just means that you should focus on learning those skills before really digging into her playstyle.