L5973 (step down) used in constant current oscillates
Section 3 of your linked document is the classical approach to current regulating an LED because of its simplicity and, clear compliance with rules that govern the L5973 (and most other chips of this type) in order to keep the feedback loop stable. 

One of those rules is don’t screw around with the feedback path and, in particular, don’t add op-amps into the feedback path unless you know the general consequences and are prepared to run the extra mile to ensure loop stability.

But, you are adding two series op-amp circuits into the feedback path so you have to take great care that the loop remains stable.


  It kind of works but I get some oscillations in audible range.


I smell a whiff of instability and that instability could damage your LEDs with over current quite easily.

An alternative to your approach is to go back to the classical way of connecting your LEDs as mentioned in section 3 but allow your PWM signal to modify what is fed back to the FB pin directly and passively.

For instance, you are already converting your PWM to an analogue voltage and, if this voltage is directly fed to the FB pin via a high (ish) resistance you can “con” the chip into shutting down current into the LEDs.