Here are some things to keep in mind when requesting reviews if you're wanting to receive them quickly!
First, every reader likes to complete different types of reviews. Some prefer our Standard ("free") reviews, some prefer Kindle Unlimited, while others prefer the extra snaps that come from Verified Purchase reviews.
In order to appeal to as many readers as possible, we recommend requesting a mix of these review types. We find that typically, if an author is experiencing a long wait time, it's because they're only requesting one time of review, usually only Verified Purchase reviews.
So if you're in a hurry, try requesting a mix of reviews. They each have their own pros and cons to readers, and you'll appeal to all readers if you request all 3 types.
Hope that helps!