Now, I'm still growing as an Instagrammer, but with this method I've been able to grow from a slowly scraped together 450 (over about three years) to 700 in two months, so I think it's safe to say this method is reliable for natural growth! So here's what I do:
Do not post daily! A lot of things tell you to do that, but they are outdated. The algorithm was changed to kill content farms and spam bots. Now it rewards you for posting like a normal human (a few times a week). I post on Wed, Thurs, and Friday, but post on your most active days!
Turn yourself into a business profile! This will show you what is performing the best, why, and if people went to your profile or followed you because of it. It will also let you see what days your followers are most active for the above tip.
Tags are tricky. DON'T USE ONLY THE MOST POPULAR TAGS. Use a few of those, and then seek out tags that have between 10-500k posts. then a few that are 1-10k. Popular tags are good for getting instant attention, but only for about 10 seconds. You want a good number of slow burn tags too, so your post will hang out in the "recent" section for a while.
Don't post the same thing every time with the same tags. The algorithm reads this as potential spam. I instead spice it up with different stuff every week. People will enjoy it more and ig will show it to them more. try not to use the same tags two posts in a row.
Post videos! Process videos, videos of your art sparkling when you use sparkly paint, videos of you mixing paint. Videos are priority on the discover page. You will get more attention for you.
Stories are where you can get your interaction esp early on. Follow people, watch their stories, reply to them. Join the community. People love to talk, and talking to ppl boosts your engagement. Use your story to talk to your followers. Share posts you like there. You make friends this way.
Like and comment on other people's posts! Especially people who post things you post. ESPECIALLY if you just used the same tag they use. Get you icon and username on any post relevant to you with personal comments and likes!
People will love ocs here. They care about ocs on instagram. POST YOUR BONUS CONTENT!! Fanart only does well if you grow yourself in that fandom deliberately. It's not a free attention card like most places.
Bonus: Do instagram art challenges. You have to @ the creator, and then they'll also share your work! It works wonders. People esp love "draw this in your style".
Share any tips your know! I'll add more as I think of them.