Is it permissible to marry the daughter of one’s father’s paternal uncle?

Yes, it is permissible for your brother’s son to marry that
woman, because in fact she is also regarded as the daughter of a paternal
uncle for him as well, because his father’s paternal uncle is also a
paternal uncle to him and to his children after him. Allah, may He be
glorified and exalted, says (interpretation of the meaning):

“O Prophet
(Muhammad (blessings and peace of Allah be upon him))! Verily, We have made
lawful to you your wives, to whom you have paid their Mahr (bridal money
given by the husband to his wife at the time of marriage), and those
(captives or slaves) whom your right hand possesses – whom Allah has given
to you, and the daughters of your ‘Amm (paternal uncles) and the daughters
of your ‘Ammah (paternal aunts) and the daughters of your Khaal (maternal
uncles) and the daughters of your Khaalah (maternal aunts)”

[al-Ahzaab 33:50]. 

Shaykh ‘Abd ar-Rahmaan as-Sa‘di (may Allah have mercy on him)
said: Similarly, one of the things that Prophet (blessings and peace of
Allah be upon him) has in common with the believers is the words: “and
the daughters of your ‘Amm (paternal uncles) and the daughters of your
‘Ammah (paternal aunts) and the daughters of your Khaal (maternal uncles)
and the daughters of your Khaalah (maternal aunts)”.
That includes paternal uncles and paternal aunts, and maternal uncles and
maternal aunts, whether close in degree or otherwise.

End quote from Tayseer al-Kareem ar-Rahmaan fi Tafseer
Kalaam al- Mannaan (p. 669)

For more information, please see the answers to questions no.
34791 and 112320

And Allah knows best.