。
She shot him an angry glance.
Literal
She [topic-は] him [object-を] anger [genitive-の] eye [with-で] glancingly looked.
怒りの目で ('with eyes of anger') uses the instrumental で to mark the manner of looking — the eyes are the 'instrument' of the glance. ちらりと is a 擬態語 (state mimetic) for a fleeting, momentary glance — the と is the adverbial と that attaches to mimetics to turn them into manner adverbs modifying the verb. Together the phrase paints a sharp, brief glare rather than a sustained stare — the visual equivalent of 'shooting a look.'