"The inward eye" I believe just refers to one's ability to imagine or remember visual things in one's mind. To "flash" here just means to occur quickly upon the senses. Just as something might flash upon your physical eyes (meaning you see it briefly), here the English suggests some visual that flashes (briefly appears) to one's inward eye (his ability to imagine visual things).

William Wordsworth "I Wandered Lonely as a Cloud" "They flash upon that inward eye." Wordsworth makes use of metaphor in that line. A 'flash' represents a reoccurring vision of daffodils that the poet experiences inwardly. It expresses the peace of solitude that was experienced in a place and is re-experienced 'upon that inward eye' (a place that is deeply spiritual to the writer).