Sark does not have a flag in the game, no. You can actually check yourself what flags are in the game.
https://warzonecdn.com/Images/Flags/VA.jpg is Vatican City for example.
They just used the ISO 3166 alpha-2 codes. So a couple interesting flags in the game that will probably never get the achievement:
Bouvet Island (literally has 0 people living here, but still got a flag in the game. And believe it or not, it's very slightly different from the Norway flag in the game, despite being the same irl)
Guernsey (just a cool flag)
South Georgia and the South Sandwich Islands (More penguins than people)
Guam (interesting design, although not very creative)
Heard Island and McDonald Islands (again with a population of 0. But this time identical flag to Australia)
British Indian Ocean Territory (Again a population of 0, but with some military there)
Pitcairn Islands (35 people live here, but they have a tennis court. They might have the most tennis courts per capita)
Svalbard and Jan Mayen (they again have a different flag than Norway or Bouvet Island in the game, despite them using the norwegian flag irl)
Kiribati (a place with lovely city names, such as London, Paris, Poland and Banana)