Israelites are "the children of promise", "begotten of the spirit", and "spirit"
Ishmaelites are "begotten of the flesh"
In order to fully appreciate what's meant by "flesh" and "spirit" im the following verse, we must understand what Paul meant by his allegory in Galatians 4:
Follow this carefully and you'll understand that:
The bondmaid is Hagar, Sarah's Egyptian slave, her son is Ishmael whose descendants are the Arabs. The freewoman is Sarah, her son was Isaac, and the everlasting covenant God made with Abraham was through all the descendants of Isaac's son Jacob.
The everlasting covenant God made with Abraham through Jacob preceded the covenant at Mount Sinai. Paul is equating the everlasting covenant to Jerusalem [read: Israelites] and the covenant at Mount Sinai to Arabs.
"Us all" must be a reference only to genetic descendants of Jacob, and in this instance only to the "house of Israel" which is the twelve northern tribes.
There were more descendants of Ishmael whose mother Hagar was "desolate" than there were of Jacob whose grandmother Sarah "hath a husband", Abraham.
"The children of promise" is the phrase used to refer to genetic descendants of Isaac (and specifically to genetic descendants of Isaac through Jacob, as God hated Esau and excluded his descendants the Edomites from the covenant).
The Arabs who were "begotten after the flesh" persecuted the Israelites [read: "the children of promise" who are now equated to "begotten after the Spirit"].
While God blessed Hagar and promised Abraham that her that her son Ishmael would "twelve princes shall he beget, and I will make him a great nation", her descendants were not heirs to the evelasting covenant God made with Abraham through Jacob.
This is proof that Paul is addressing only Israelites here, not Arabs who were "born after the flesh", nor jews who were descendants of Esau who God hated, nor mamzers who cannot ever enter the congregation of the LORD, nor nokriy who God commanded the Israelites to "save alive nothing that breatheth". His point is that, just because Arabs and Edomites are descendants of Abraham by "flesh" [through Ishmael or Esau] doesn't mean they're descendants "by promise" or "spirit". If you're not a descendant of Abraham through Jacob [read: an Israelite], then you're not "by promise", "children of promise", nor "born after the spirit".
The jews claimed to be genetic descendants of Abraham. Jesus agreed, but said they were not "Abraham's children". This reference to "children" means "children of promise". This can only mean that Jesus knew that the jews were Edomites who were descendants of Abraham through Esau, and thus were not "children of promise".
Conversely, only those who are pure genetic descendants of Jacob have the potential to be "children of promise"--but obviously many of them ARE NOT, and never can be. Young's Literal Translation eliminates the words the KJV added (which we know they added because they italicized them), providing the following translation of Galatians 4:29:
This might have been a sincere attempt by the KJV translators to make this verse comprehensible, but by adding these five words "that was born" and "it is", they headed in the wrong direction. YLT gets us back on the right path--but it's not a completely comprehensible statement. Our sense of the English phrase "according to" [kata, #2596] would suggest that those "born according to the flesh" persecuted "him", in compliance with instructions from "the spirit". Clearly this is not the message, so we need to put this into context with other verses, like the following quote from Jesus, to get a better sense of the word "kata":
John 3:6 That which is begotten of the flesh is flesh; and that which is begotten of the Spirit is spirit.
This does not say that those "born of the spirit" [read: Israelites], are "according to the spirit", or "of the spirit", or can "become spirit"--it says they ARE "spirit". Who did the Ishmaelites, who were "born according to the flesh", persecute? Spirit. Not those "born according to the spirit". Not "of the spirit". Spirit! Literal: perfect past tense, what happened in the past still affects today. "the one beggoten in the past and still feeling the effect today, it is out of the flesh, it is a flesh, and the one begotten in the past and still feeling the effect today, it is out of the spirit, it is a spirit".