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I assume you mean one PNR / booking with AA and BA mixed, but a return ticket VIV-LHR and back. Without specific dates and fares you can only get a possibly useless general answer.
BA can book AA fares, it's not likely to be cheaper than online, but it does have the merit of getting the Amex Avios bonus. Some fares cannot be sold by BA, they can only be sold via AA. If this is a protection issue, then AA will protect AA's end of a booking if there are delays. Broadly speaking however (and specifics will vary) through ticketing brings additional protection benefits, is sometimes more expensive, sometimes less expensive. Possibly an agent will spot something which will bring the cost down over BA.com, which may well be forcing fares into expensive Codeshare buckets, for example, when Prime would be cheaper. Clearly it wouldn't cost anything to ring BA and see what they can offer, if the price is too high then then you can decline to take the matter forward.