conflict of interest

You mean “sought” not “seeked”.

The fact that the auditor has two clients who might be in competition with each other does not of itself create a conflict of interest between the auditor and clients.
In fact it is quite common for an audit firm to become expert in a particular field. So if potential client Y doesn’t like the fact that B & Co is auditing client X, they can simply not appoint B & Co (!) (Who is the auditor of any company is a matter of public record.)

Conflict might arise in different scenarios – e.g. a management team asks the auditor to advise on the terms on which it should offer to buy-out the company and the company asks the same professional accountant to advise on whether to accept an offer. Suggesting that one client seeks additional independent advice in this case probably doesn’t go far enough – and isn’t really sensible financially (if they have to pay for additional independent advice they might just as well pay only for that advice!)

Another example – let’s suppose a client is a partnership – and one of the partners wants to retire and effectively be bought out of the partnership. Who better to ask in the first place for advice than the auditor? There is no reason why the auditor cannot give some advice to the partner – but clearly the interests of the one partner and the remaining partners conflict because the retiring partner will want to take as much out of the partnership as possible. So for both parties to seek additional independent advice would be a safeguard.