No it isn’t a war crime for a each soldier not to wear a national insignia on a uniform. It’s only very recently that US soldiers started wearing a flag on their uniform.
During that conflict, the U.S. military captured thousands of Taliban and al Qaeda forces, hundreds of whom were allegedly not complying with the rules of war, failing to wear uniforms with insignia clearly displayed, failing to carry their weapons openly, and failing to organize themselves in units subject to a hierarchical chain of command.
I said nothing about specifically the national flag. The RF forces wear, I believe, the tri-color arm badge, and a double-headed eagle cocarde. Al combatants in both WWI and WWII wore distinctive uniforms with insignia of nationality, unit and rank. That they remove them is at best a military ruse, -- but then the very use of a ruse qualifies as a hostile offensive operation, not a peace-keeping or protective mission.