Using the standard colours of the Don Cossacks was my original plan. I'm quite fond of the Don Cossack flag actually, being one myself (partially) and from Donetsk no less. What I was referring to as 'hideous' were the modern flags of Donetsk and the Donbas, which are an eye-aching combination of bright blue, yellow and black.
As for why I want to know the old flags, it's simply to fit the unit's fluff. It's meant to be a fictional, local Don Cossack formation that put down socialist revolts until finally being drafted into Hetman Skoropadsky's Ukrainian army. After the latter's fall, this unit headed eastward to join the Volunteer/Don Armies, like most White Russians and Cossacks that had been in Ukraine at the time.