She read his letter with tears streaming down her cheeks.
Literal
She [topic-は] cheeks [on-に] tears [object-を] streaming [while-ながら] his letter [object-を] read.
~ながら links the two simultaneous actions — shedding tears and reading. 涙を流す ('to shed tears,' literally 'to flow tears') is a standard literary expression. The sentence has a narrative, scene-setting quality.