Yes, it does, so something like a "flesh wound" can be translated as "cneá feola", but it is worth noting that there are a lot of idioms in English that use "flesh" that wouldn't necessarily use "feoil" in Irish. It's worth reading the entry for "flesh" on focloir.ie:
feoil is just meat (or flesh). It's not a compound word, so fe isn't a prefix.
muiceoil (pork) is a compound word derived from muic (pig) and feoil (meat). When the two words are put together to form a compound word, the second word is lenited, so we have muicfheoil (pig meat). The fh is silent, so at some point in time the fh was dropped altogether giving just muiceoil.
In the same way, mairteoil (beef) comes from mairt (a slaughtered cow or bullock) and feoil (meat) = mairtfheoil (slaughtered cow or bullock meat) = mairteoil, with silent fh dropped.
This sound is difficult to hear clearly because the speaker says it so quickly. Slow down and live and I might have a chance of learning something. Is she saying something like "fell-wee"?