My Instagram profile is mostly focused on art, so I can't guarantee that these suggestions will work for writers too, but here's a few things you can try:
-Find the right time to post. Seriously, time seems to be EVERYTHING on Instagram. From my own time zone (CET), I found out that 10.00 AM to 12.00 PM are pretty much the only hours any of my posts are going to be seen, with 12.00 PM being the "most productive" time. A minute earlier than that or a minute earlier than that... and all the magic is gone XD for real, I posted about Inksgiving at 5 PM once, got zero likes. Posted the same exact thing one day later at 12 PM, got 22 likes.
-SPAM WITH TAGS :'D I don't remember how many tags exactly you can use on Instagram, but you can have... quite a lot. Surely more than on most sites. Use as many of them as you can think of. Start writing something and look for related tags: writersoninstagram, instawriter, instawriters, amwriting, amwritingromance, use ALL the variations. The more, the better!
-Go on a "like" spree as soon as you post something. Forget about the popular posts, though. Check a tag you used in your own posts and look for recent posts in that tag. Then start liking posts like there's no tomorrow XD (...tbh, I try to "like" posts I actually enjoy when I do that and not just mindlessly clicking whatever comes up, but if you're on a rush, I guess it wouldn't hurt liking random posts as well). If you find a post you really like, check the profile of the person, see if you find anything else you like and click that heart button (I actually found quite a bunch of really nice artists doing this!) Sometimes, people whose posts you liked will come back to like your posts too. Some will also follow (small profiles especially).
I did all three of these for about a couple of weeks when I first created my Instagram account and got almost 200 followers doing so. Granted, my numbers got pretty much stuck there afterwards because I got lazy and stopped doing it, but doing so still helped building a little bit of following hope that helps!
Also, some suggestions for "visual" kind of posts that you could try as a writer:
-Desk/workplace. Basically, a pretty picture that shows the desk you're working at. Stuff like this or this. Don't have a nice desk to show off? Use a creative angle :'D My own desk is A MESS. But thanks to close ups and a few arrangements... here it is, looking all nice and clean
-Moodboards. Basically, a collage of pictures that represent your characters, scenery from your story, or anything else you can think of. Just make sure not to use copyrighted stuff or artworks you don't have the permission to use to avoid troubles. Pixabay and Pexels are great sources for free pictures you can use.
-Handwritten quotes. Same as digital quotes, but with a more personal twist. Bonus points if you have a nice handwriting and/or can make your pic look "aesthetic", kinda like you can see in this post.