The Chinese government forces the Uighur Muslims in East Turkistan to put the Chinese flag inside their mosques, above the minbar or on the qiblah wall.

Is it permissible to pray in these mosques?

Please note that the Muslims there are weak and oppressed. They do not want to put these flags in their mosques, but it is the government that forces them to do that.

Praise
be to Allah.

It is not permissible for the
Muslims to forsake the houses of Allah, may He be exalted, even if the
flags of kufr and symbols of oppression are placed in them. The Muslims
have more right to their mosques than any other people on earth, and jihad
is ongoing until the Day of Resurrection, both verbal jihad and the jihad
of swords and spears, and jihad to attain freedom and dignity, so that the
people may live happily under the rule of Islamic sharee‘ah. 

If the Muslims were to refrain
from praying because of a flag that has been placed above the minbar, then
they would have granted their enemy the greatest of victories for nothing.
Their enemies are scheming by night and by day to prevent them from adhering
to their religion, to assimilate them, and to distort their beliefs and
their faith. So what Muslim minorities must do is be aware of such tricks,
and not be deceived by fatwas that tell them not to pray in places where
there are images and symbols of kufr. Those fatwas have a basis in truth,
but they are applicable in situations where there is freedom. But in cases
of need and necessity, where there is a confrontation with oppressive
authorities, then there is a particular ijtihad in such circumstances, in
which pros and cons are weighed up, and the focus is on real circumstances
rather than symbolic matters which one can do without. 

Before the hijrah, the Prophet
(blessings and peace of Allah be upon him) prayed in al-Masjid al-Haraam,
despite the presence therein of the idols of the Jaahiliyyah. Those idols
did not prevent him from conveying the message of Tawheed and praying
openly, bowing and prostrating. The truth that he conveyed was stronger than
the falsehood that was prevalent in that place. The one who follows the
truth should be proud and confident, and not give up his position, no matter
what the circumstances. That is what had a great impact on the progress of
the Prophetic call. 

See also the answer to question
no. 201083 

And Allah knows best.