To my knowledge, the only mainstream issuers that will approve you soon after BK are Capital One and Disco. I would counsel being patient and waiting at least 6 months before applying for a new card. If you want to build up more of a record the subprime cards such as Credit One and Merrick are always a possibility.
Another way to build credit relatively quickly is to apply for one or even two secured credit cards; this was the approach I took after my discharge. Keep in mind, not all secured credit cards are created equal, and not all are allowed to graduate to unsecured, and to take it one step further, some of those which are advertised to graduate take their sweet time doing so (often years). The approach I took was to open a secured card with my bank; it graduated almost exactly 6-months to the day after my first charge; it became unsecured two years ago next week and has already had its limit increased significantly (as in more than 2x) since that time.
As mentioned above, patience is key when rebuilding; take your time, do your due diligence, and choose the right cards for you, secured or otherwise.
