Sacrifice a couple points and manually request a CLI on it.
Starting Score: 512
@Bill77 wrote:I think your odds are better trying to get a 2nd non-Amazon Chase credit card and moving some of that CL over to the Amazon card if you get approved. I'm not even saying you will be approved only that your odds are better because the luv button has already spoken several times.
I may give that a try. They pre-approved for a $60,000 auto loan on a sp, so there is some luv there 
@Brucemac wrote:I don't know why but I cannot get Chase to show me any love on my Amazon prime Visa card. I've had for 1 year at $3000 cl. Every time I press the love button it says no offers available. Anybody have any trucks or advise? I've received many CLI on all my cards but this one. I put a lot in this card and pay it down. Score average 749
I didn't even know there was a "love button" for Chase cards. Where is it? I've never seen it.
Never mind. I found it. More > Account Services > Request a Credit Limit Increase
For a while there, they were handing out auto-increases with heavy usage, however it's been a minute since I heard of it happening with the frequency of 2021/22. I finally gave up and closed my Chase Amazon card last fall. It had been at a $1000 limit for 7 years or so... ridiculous. Really Chase? 
Auto CLI from Chase seems to be a hit or miss for me. I have my Chase Flex (started out as Freedom Student) since Apr 2020 which started out at $1k. With the benefit of having 6 PIFs within the first 12 months did an auto CLI -> $1.2k CL now. I had the card for easily 2 years and haven't inch another CLI any time soon.
I was over 5/24, but since I had a history with Chase I tried my luck with Chase Amazon card and nailed a solid $10k CL and lowest APR (Open on Aug 7, 2022). In Jan 2023 after the statement, I noticed during my account review a bottom notif. (Chase App) stating they have increased the CL -> $12.5k CL ... nice surprise and I only put down roughly $4k-$5 within 5 months.
Comes this month and I am under 5/24 ... Feb 1, 2023 pulled for a Chase Freedom Unlimited and nailed $16.4k CL with lowest APR+2% more.
My guess auto cli can happen whenever. But I scored more now that I can balance my unlimited and flex card in a few months.
@SouthJamaica wrote:
@Brucemac wrote:I don't know why but I cannot get Chase to show me any love on my Amazon prime Visa card. I've had for 1 year at $3000 cl. Every time I press the love button it says no offers available. Anybody have any trucks or advise? I've received many CLI on all my cards but this one. I put a lot in this card and pay it down. Score average 749
I didn't even know there was a "love button" for Chase cards. Where is it? I've never seen it.
Never mind. I found it. More > Account Services > Request a Credit Limit Increase
Apparently, that button still remains a mystery on DPs. Although it was mentioned on myfico, my guess it does follow the 5/24.