a) It seems as if the flag of the new republic represents the old empire. -->correct
, "it" in the sentence is called paceholder it .
b) The flag of the new republic seems as if it represents the old empire. -->there is ambiguity regarding the usage of it . It in the sentence can refer either to the republic or the flag
c) The flag of the new republic seems as if the flag represents the old empire.-->the usage of flag in the sentence is reduntant .
+1 if you like my explanation .Thanks