This option can provide many advantages. But to benefit from these, keep three tips in mind:
How broad is your potential provider's recruitment reach? How many different channels do they actually use to advertise your vacancy? Checking their reach will reveal whether you'll attract the best of all the available candidates, both those who are looking'(active)'- and those who aren't (passive).
Are they as up to date with recruitment as they are with recruitment technology? Is their approach conventional or more cutting edge? Assessing their level of expertise will help bring in the right new recruit.
Look at how much your potential flat fee provider wants to get to know you and your goals. Do they take the time to get to know you? This is good commercial sense, not just good customer service. Choose a provider who asks you detailed and high quality questions and you're much more likely to enjoy a high quality response when you're advertising a vacancy.