How to get music from Dropbox to ANY mp3 music type app
It's really not possible to get music from Dropbox into the music app on your iPhone. Apple does not support getting music onto your iPhone that way. The Dropbox app will play the songs but is hardly a music playing app.

You mention Linux. Do you have a Mac or a Windows PC? The best way is to add the songs to iTunes on a Mac or Windows PC and then sync your files using iTunes. Apple does not make iTunes for Linux and iTunes is the only supported way to get music from your computer onto your iPhone.

Not being a Linux guy there may be a Linux application that will get the music onto your iPhone without iTunes. Maybe there is a Linux guy here that knows if there is such a thing. I don't know, sorry.

Apple is all about making it simple to do basic things for the majority of people. Those of us at the geeky/nerdy end of the spectrum often face these frustrations. You can either continue to be frustrated, or just relax and do it the Apple way, using Apple software. There are a number of things that have always annoyed me about Apple software and Macs (+ iPhones...) in general. But I have learned to accept the limitations because I don't like Windows and Linux just annoys me. But that is just me, you have to do what works for you.