@matthilt There’s a number of ways of doing this typically under the titles of POSSE or PESOS. Some for WordPress are documented here: https://indieweb.org/WordPress/Plugins#POSSE_Plugins
Specifically for Instagram, I think the majority use OwnYourGram.
Typically the more control you want over output for syndication means a bit more work upfront, while the easy solutions give you less control over how things look. Feel free to ask for opinions in chat as well either in the main channel or the #WordPress channel.