From Wikipedia's article on the flag of Novorossiya:
Ukrainian political analyst Mikhail Pavliv is credited with having created the flag; Pavliv explains that he had simply stumbled upon the flag online somewhere, and that the leader of the New Russia Party, Pavel Gubarev, later picked it up. However, Gubarev has stated that the inspiration for the flag came from banners used by Cossacks in the 18th century. According to Alexey Eremenko of The Moscow Times, no Cossacks ever used a flag resembling the one chosen.
I'm not totally convinced by either of those origin stories, but they make a lot more sense than 'right-wing assholes' getting together with Putin and being like "You should totally use the Confederate flag. No one will notice. It'll be our little secret. Tee-hee-hee."