There is no ‘historical flag of the BRD’. The current Federal Republic of Germany (German abbreviation: BRD) is contiguous with the state that was founded in 1949. The only changes to the federation were the reorganisation of states in the South-West (creating Baden-Württemberg out of three predecessor states) and the admission of the Saarland in the 1950’s followed by the admission of 5 states that formerly made up the GDR plus the enlargement of Berlin (accompanied by a status change for former West Berlin) in 1990. At none of these points did any grand scheme of the state change; most notably, constitution, national flags and national anthem remained the same throughout.
As Martin Schröder outlined, the black-red-gold flag is the official civil flag of Germany and has been since 1949. One version with an eagle shield is a state flag (although the plain black-red-gold is also sometimes used as a state flag); another version with an eagle is apparently an unofficial variant but I daresay that the majority of citizens would not know the difference.
An ambassador in their office would most likely have a state flag with the eagle on display as it seems slightly more official than a mere civil flag (and because they have the authority to use it). Most flags flying outdoors (e.g. on the Bundestag) will be the civil flag (citation needed).
It’s worth noting that these two are not the only black-red-gold flags with a coat-of-arms on them. As Wikipedia’s list of German flags shows, three German states (Lower Saxony, Rhineland-Palatinate and the Saarland) use a black-red-gold flag with their state coats-of-arms on top (Rhineland-Palatinate in the canton, the others in the centre). But more importantly and controversially, the flag of the GDR was also black-red-gold but including the hammer-and-compass symbol of socialist East Germany. This last one, obviously, has quite different implications from any of the above which are just ‘I like my country’ or ‘I support my national football team’.