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Discover prequal, or did you burn them too? Cap One rarely rarely black lists. I've seen consistent posts here from people who burned them for a lot and got back in immediately. I burned them for about 1500 and got back in around 16 months.
The CL with a secured Discover Card is simply going to be whatever you deposit. You can add money during the time you have the account up to a max of $2500. So if you do prequal again, just take it and deposit what you can. You can add more later if you need to.
Cold apping coming out of BK is dangerous in my opinion. It's a great way to waste inquiries and probably not get approved. I would not do it, personally.
As for Kohl's, the preapproval could be legit. Even though it's a Cap One card store cards are different than the core cards. You only need 3 cards to improve your credit. If you have them it might be worth waiting. Are you trying to get out of AFs? I would hold off on Barclays for awhile yet, but that's just me.