I try casually skimming through the book that Reiko recommended, right there on the spot.
Literal
Reiko [possessive-の] recommendation [called-という] book [object-を], that place [at-で] lightly skim-reading do-[try-てみる].
オススメ (katakana おすすめ) is the casual noun form of 勧める ('to recommend'). 流し読み ('flow-reading') means skimming — reading by letting one's eyes flow over the text without deep engagement. ~てみる ('try doing') signals this is an exploratory, non-committal action. その場で ('on the spot, right there') emphasizes the spontaneity.