The length of time will have no impact...
You DO need to wait for the new statements to cut, and for the CRA's to update. As you mentioned, you'll see quite a score boost when that happens...you'll know. 
I would pay down your cards to < 30% utilization and let them report before I applied. You might consider paying down your cards every week so to avoid utilization > 30% which is what causes you to take a hit on your FICO scores.
Are you applying for an Amazon Prime Store Card or a Chase Amazon Card?
@tcbofade wrote:The length of time will have no impact...
You DO need to wait for the new statements to cut, and for the CRA's to update. As you mentioned, you'll see quite a score boost when that happens...you'll know.
Exactly. Dropping the utilization is the fastest way to initiate a score increase.
@Anonymous wrote:
I currently have two cards, a Wells Fargo Platinum with a $550 limit, and a Capital One Quicksilver with a $750 limit. Between the two I’m at about 98% utilization. I plan on paying them down to about 20% utilization within the next week. I’ve had both of these cards for 5+ years and they’ve been close to maxed the whole time.
According to Credit Karma (which I know isn’t exactly reliable) my TU and EQ are at 627 and 626. Other than my high utilization my credit slate is clean (current on car loan and cc payments; no collections, hard pulls or judgements), so I’m assuming paying them down will raise my score quite a bit.
I would like to open an Amazon Prime Card, but I’m curious as to how long I should wait before applying. Can I apply as soon as my credit score updates? Or will the length of time that I’ve had high utilization effect my approval odds even after they’re paid down?
Yes paying them down to 20% will help your FICO scores quite a bit.
I have no opinion on whether you would be approved for Amazon Prime at that time, but the length of time you've had high utilization will NOT be factored into the decision.
It is in your favor that you have a good average age of accounts, a good age of youngest account, no recent applications, and not too many accounts.
It might cut against the size of your starting limit that your credit limits are low, but I don't think that issue is as important with the Amazon Prime card as it is with Chase branded cards.
