。
She's easily swayed by emotion.
Literal
She [topic-は] emotion [by-に] swept-away-easily.
情に流される (じょうにながされる) is a set expression: 情 ('emotion, feeling, sympathy') + に (agent/cause) + 流される (passive of 流す, 'to be swept away'). The ~やすい suffix means 'easy to, prone to.' Together: she's the type who easily gets carried away by feelings. This construction treats emotional vulnerability as a tendency.