。
She spoke to me in English purely to show off.
Literal
She [topic-は] flaunt only [purposive-のために] English [in-で] me [target-に] spoke-to.
見せびらかす is a punchier word than the simple 見せる: it carries the 'flaunt, parade around, show off ostentatiously' nuance, often disapprovingly. The structure ~だけのために compresses two ideas — だけ ('only / nothing but') plus ~のために ('for the purpose of') — into 'purely / solely in order to.' 英語で uses the instrumental で ('by means of'), the same particle that gives you 箸で食べる or 電車で行く. The compound 話しかける is built from 話す + ~かける and means 'to speak to / address (someone)' — the ~かける aspect carries a 'direct an action toward' nuance, the same family as 呼びかける ('call out to'). The masculine ぼく gives the speaker an unassuming, slightly boyish voice.