When the Weimar Republic's black-red-gold flag was abolished in 1933, the Nazi flag and the old imperial black-white-red flag became co-national flags. From 1935 on the Nazi flag was the sole national flag. The popular myth is that this was a response to an incident where some Americans boarded a German ocean liner in New York Harbor and threw the swastika flag overboard, and the United States government refused to take any action because it was only a political flag.

The dual flag arrangement was pretty atypical, but that's because there were two flags, not because one of them was a party flag. Actually it's pretty common for political flags to become national flags. Laos flies the Pathet Lao flag, Guinea-Bissau flies the original PAIGC flag (and Cabo Verde used to fly a similar one), Mozambique's flag is the old FRELIMO flag with an added emblem, Palestine uses the PLO flag, São Tomé and Príncipe uses the MLSTP flag, Taiwan's flag incorporates the Kuomintang flag, Timor-Leste's is based on FRETILIN's, Angola's is based on the MPLA's, Zimbabwe's is based on ZANU-PF's, Zambia's is based on UNIP's, Kenya's is based on KANU's, and the Indian flag is based on the old Congress flag.

You'll note that most of these countries are former colonies -- and specifically African colonies -- that won independence after World War II and then adopted the flag of their liberation movement. So you could say that Germany is a bit unique in terms of both its time and its place. But using a political flag as a national flag is far from unheard of.