In the King James Bible, the possessive pronoun forms mine and thine appear before words beginning with a vowel. (The indefinite article an is the last remnant of this alternation in standard English.) Here Oliver Cowdery initially wrote “mine flesh”, but later he corrected it to “my flesh” by crossing out the mine and supralinearly inserting the correct my. The ink flow for the correction is heavier and darker; the quill itself appears to be broader, suggesting that the change occurred considerably later (with either a different quill or the same quill now worn dull). Oliver made a similar kind of correction of iniquity to iniquities in the next line (see the discussion immediately below). Since there is no grammatical reason to change the singular iniquity to the plural iniquities, we may deduce that both that change and the preceding change of mine to my were probably the result of proofing 𝓟 against 𝓞. Thus we may assume that the original manuscript (although not extant here) read “my flesh”.
Oliver Cowdery’s original error in 𝓟 was probably caused by the mine of “mine iniquities” in the parallel sentence that immediately follows:
Elsewhere the text has only “my flesh” (nine times), including three more here in 2 Nephi 4:
We also have evidence that Oliver Cowdery tended to accidentally write mine when prompted by a nearby mine, as in the following example when once more a parallel construction is involved (“Sam mine elder brother” followed by “Jacob and Joseph my younger brethren”):
Thus internal consistency and manuscript evidence support interpreting the initial “mine flesh” of 2 Nephi 4:17 as a scribal slip, influenced by the following “mine iniquities”. For further discussion of my versus mine (and thy versus thine), see possessive pronouns in volume 3.
Summary: Maintain in 2 Nephi 4:17 Oliver Cowdery’s correction in 𝓟 of “mine flesh” to “my flesh”; all other evidence in the text suggests that my, not mine, is the correct form before flesh.