If a person is truly brain dead then no they should not feel any pain since your brain uses signals from your nerves to feel the pain.
To be declared clinically brain dead the person must not be able to feel any pain as well as the person should not respond to external stimuli.
If the person feels pain then they may only be partially brain dead and not completely brain dead since if a person is completely brain dead then no pain should be felt.
A person could have partial brain damage that may put them in a Coma and they might seem like they're complete brain dead but if they feel pain and respond to pain then they're not completely brain dead.