Since IFTTT can consume any RSS feed, you can just use any client that lets you export your starred articles as one, such as Tiny Tiny RSS.
I have a similar use case, where I want to automatically download chosen podcasts. I just created a "download" label, got an RSS feed link from my client and put it on a podcasting app. Now I just need to label the episodes I want to listen to on Tiny and they'll be automatically downloaded to my phone.