I also have an affiliate program where I pay a flat rate commission per lead. However, since I need high-quality reviews quickly, I'm leaning towards requesting sponsored posts rather than an affiliate partnership with top review sites in my industry.
Depends on their media reach and the kind of audience they have. Think of it as any other form of advertising - TV, radio, etc all set their pricing based on those two critical factors.
If your audience are hard to target traditionally, then it'd make sense that you spend more per audience member than with a broad technique than TV advertising.
I'd suggest you work with the content creators, and try to come up with an amicable price.
However, with a blog with less than say - 10K readers, I'd guess around $150 USD. Up to $700 for up to 100K readers, and $1200 for up to 500K readers. These are rough ballparks and vary, but gives you an idea.
Don't start with the price for a review, start at the end. How much do you intend to make on an acquired customer? That's your LTV.
Then, figure out what you intent to pay to acquire that customer. A good rule of thumb is 30% So if you are going to make $100 / customer, LTV then you can spend 30 in customer acquisition cost.
Finally, figure out how many customer you think you can convert from a paid review. Multiply that times your CAC and that's probably a good number.
Of course you don't really know if that's what you will convert so this is all just speculative. The point is you should always go through an exercise something like this before you blindly spend advertising dollars.