I believe that is talking about those who will "flee" to a place of safety DURING the mid-point of the trib, for the following reasons:
1) the BEGINNING of birth pangs (Matthew 24:4-8 and elsewhere) occurs during the first half of the trib, and correlate with the seals of Revelation 6, which we know occur during the trib... and is not talking about what will happen BEFORE the trib (i.e. rapture, etc)
2) a resurrection (in this passage, FUTURE, i.e. "shall arise") occurs AFTER the trib, that of OT (and trib) saints (Dan 12:1-2, 13)
3) the phrase "My people," in the OT, means Israel
4) there will be a believing remnant of Israel, in the trib (in Matthew 24:15-21), Jesus tells them (which are in Judea) to "flee" when they "see the abomination of desolation" (they will "be hidden" in safety in Petra/Bozrah; Rev 12:6, 14)... before that, they are told not to believe the false Christs (verse 5) and false prophets (verse 11)
5) "the hour of trial" (Rev 3:10) is the first half of the trib, specifically; and, "the hour of judgment" (Rev 14:7) is the second half of the trib
6) the "delivery" (of the birth pangs) is their promised/prophesied earthly Millennial Kingdom
That's how I see it.