how to measure phase response of filter
Feed the filter input from the sig-gen. Terminate the filter output appropriately, either into one channel of the scope, or an appropriate load.

Use one scope channel to measure the filter input, use the other channel to measure the filter output.

Take care to respect the filter loading, and the symmetry of the two channels. If you terminate the filter in a 50ohm scope channel, you should pick off the input with a 1k(ish) resistor, and run that into the other channel at 50ohm. If you use high impedance scope probes, try to use identical ones, on the same setting.

There are several ways to interpret the scope display. One is to eyeball the two traces and estimate the phase shift. Many digital scopes have a Phase(Y1,Y2) function that will do the job for you. If you route the two inputs as X and Y, then the scope will draw an ellipse from which you can determine the phase shift (look up Lissajous curve, wikipedia). However, make sure the bandwidth of the two channels is identical, not all scopes maintain the same bandwith and hence phase shift through the X and Y routes, you can calibrate it to check with an identical signal into each port.