Chase won't touch you until you have a year of history under your belt. If you really want a Chase card, you need to stop. They won't approve someone who's opened 5 cards in 24 months (5/24). You're already at 4.
Welcome, @Anonymous. 
You've done a good job so far. Chase likes it to see your oldest card become a year old. And they're sensitive to new accounts. Given that you're at 4/24 and you have an interest in Chase, garden until your oldest card is a year old and your youngest card is six months old. At that point, I think they'd be very happy with your profile.
Once your AMEX cards are 61 days old, you can choose one of them and request a credit limit increase to three times its current limit. I'd submit the request on the card with the higher limit unless the other one is overwhelmingly more useful.
Here's a thread that explains the AMEX 3X CLI:
The Definitive Amex 3X CLI Guide
It's huge. I'd suggest reading the first few pages and the last few pages. Then hop into the conversation and ask any questions you might have.
@Anonymous wrote:Hey everyone, I am 18 and have had a job for almost a year now. I make a bit over 50k a year and my dad got me started on the road to credit by placing me as an user on 2 of his Amex cards. He also opened a Navy Federal account for me the day I turned 18. So now I have the navy fed card and I recently opened 2 Amex cards. Where I messed up is applying for a PayPal card. I was approved but only for 300. My 2 new amex accounts were 1k and 2k. I think I have too many new cards now to apply for chase. Should I just garden now or apply for another good card since my aaoa is not really taking a hit as my credit is so new anyway? I could ask my dad but I want to show him I am learning as he always stresses the importance of good credit.
The fact that you got a $300 credit limit is a strong message that you need to garden now.
Wow, 50k at 18. Nice. As others mentioned. Slow down and take your time. You've got all the time in the world ry led to build up your credit nicely. You've already got the 3 cards recommended to optimize your score maybe get a small loan to help credit mix. 50k will set you up for some nice limits, just take it nice and slow
You are doing great, OP! I am very impressed. Just garden for six months to a year. Lenders like to see you that you are actually using the accounts you have, not applying for more within a short period time and not using them. 
You will be a myFico achiever in no time!
@Anonymous welcome to the forums! Great advice so far. I'm also curious as to when you were added as an AU on the two Amex cards? Since Amex stopped backdating accounts a few years ago, if you were added on in the past 2 years the account opening dates on those would also make them count for Chase's 5/24 policy, putting you at 6/24.
Good catch by @K-in-Boston. Unfortunately, AUs don't help one get a Chase card. But they can hurt your chances.
@Anonymous, maybe your goal should be to work your way under 5/24 over the next 18 to 24 months, then try to stay there. I don't know your current account ages, but you could probably still app for a card or two over that time period and still be in good shape once your oldest cards reach two years old.
You might also want to look into removing yourself as AU on your dad's AMEX cards, provided that they drop off your report. Others here can advise you on how to do that. The AUs have done their job by helping you with your initial apps. I think that now, you'd be in good shape to apply for credit based on your own cards (once the time comes to apply again). The critical thing would be to have the AUs disappear from your report. If that isn't going to happen, I'd let them be.
The main thing is that you have some nice cards to work with right now, though. You've bypassed secured cards, and more importantly, you've bypassed predatory banks and store cards.