Linear Frequency Dependent IQ Distortion
What you describe, phase being linear to frequency, is just a linear-phase system.

We usually design FIR filters that way, because it leads to constant group delay and hence, a lack of dispersion.

Anyway, any FIR filter that has symmetrical (complex case: hermitian symmetry) in its taps does that.

The flat response in amplitude means you're looking for an all-pass filter. There's plenty literature out there on the design of FIRs.