You can start by looking on this site for Legal Malpractice attorneys who are licensed in DC. If you cannot find at least four attorney to call, look on another site.
Before telling the attorney the details of your case, ask if (s)he knows the attorney who you intend to sue.
Consultations are protected by the attorney-client privilege unless otherwise noted.
Fortunately, you are in DC. There are too many attorneys to have this small private club that would lead and attorney to "protect their own." Nevertheless, you should make sure the attorney you choose has several years of experience and success in handling legal malpractice claims.
LICENSED IN DC
Not a Legal Malpractice Attorney