Without knowing any past derog's. Lates, CO's, ect. For best scoring you need 3 cards. You have a installement loan, so no need for another. I'd hit up Cap1 for 1 more card (Not a QS1) or talk to your bank to see what they have for you. Right now the util isn't helping at +50%. You need the have 0% on 1 card reporting and less than 8.99% on the other. Use them all you want but they have to report as I stated. There might be some past things that are holding your score down. Post them and that would help us figure a way to get your scores higher. Took me over 3 yrs to get where I'm at now. You should be in the same area as me. So list your baddies before and after BK and we'll go from there.
Well until you can get on CK. Remember the scores dont mean much but the info means alot for EQ/TU. Creditwise is Vantage. I'd call Disco and see why you cant get your TU FICO score. You can also get your EX FICO for free at disover scorecard. So thats 2 FICO scores. It looks like you need 1 more card to complete the trifecta since you got an installment loan. So right now your util is high on two cards. FICO likes 50% or less reporting balances. So there's some points. How long have you had the Disco? If its over a year or close to. Try the pre-qual and see if you qualify for a 2nd card. If so. I took my first Disco iT and converted it to the Chrome for 2% gas/groceries. That will complete the 3 for best FICO scoring. Plus its usually a single HP. If you can get the 3. Follow the AZEO method. You should pass the 700 mark then.
You've come to the right place for help. 
My first thought when you told your FICO score (640) is it's not that bad. (I am a little shy of that myself right now!) Compared to being in the mid-500s (like a lot of us were—or perhaps still are), 640 is awesome and can only go up! Sure, things start to get really good when you hit 700, but 640 isn't that bad, honestly.
You should be able to qualify for another Discover It or see if you prequalify for a Capital One product. (Probably Platinum—as has been mentioned, Quicksilver One has a fee and you can transition your Platinum over to a fee-less Quicksilver later.)
Don't despair, and look at it this way. You're already well on your way. There are not-too-bad cards that you already have or can qualify for. In six months or so you can probably get even better cards. Just keep on absorbing the advice and info here and you'll be amazed at your progress. Expect it to take time, but also remember that sometimes progress happens sooner than you think!