。
She flaunts her wealth.
Literal
She [topic-は] herself [subject-が] rich-person [being-である] fact [object-を] shows-off.
見せびらかす ('to show off, to flaunt') is a compound verb — 見せる ('show') + びらかす (an emphatic suffix) — and carries an unmistakably negative connotation in a way the more neutral 見せる alone does not. である is the formal copula, used in attributive position before こと (as opposed to the simpler ~だ which would require some adjustment in this slot — 金持ちなこと doesn't sound right, while 金持ちであること is clean). The whole こと-nominalization 自分が金持ちであること serves as the direct object of 見せびらかす — what she's flaunting is the fact of her wealth.