How to block text messages on flip phone Answered by Lively 1 year ago Top 10 Contributor Helpful ( 1) Unhelpful ( 41) Report. I like my new Panasonic phone with 2 portables, especially the Block the Caller ID button. . . Web. If you are using iPhone, tap the search tab in the lower-right corner. . . Web. . . Web. Press the navigational buttons to highlight the desired message thread, then press the OK button to select.