No, I guarantee that the flip phone does not support EVRC-NW. Though CDMA1X Advanced should not be necessary, EVRC-NW seems to have gotten wrapped up in that standard.
Regardless, the end point of your call should have no bearing on your codec in use. For example, the codec is not selected via a mutual "handshake" method -- à la dialup modems. As necessary, transcoding is applied in between the call end points. And any call that hits the POTS network gets transcoded to POTS quality.
So, a call to an old Sprint flip phone could be EVRC-NW on one end, EVRC on the other. A call to a T-Mobile phone could be EVRC-NW on one end, AMR-WB on the other -- both support HD Voice standards, but the call will be transcoded to POTS quality in the middle leg. The same holds true for your VoIP landline.
AJ