As the others have mentioned, while I am not 100% sure, I don't believe the Russian jagers did carry flags.....at least not on the battlefield anyway. I have seen loads of examples of flags for the musketeers etc.
I don't think carrying standards onto the field was a thing for many of the jager/light infantry of the period. I imagine such an item would not be overly helpful to the tactics of skirmishing!
Curious that Strelets had such a pose made for this set. Another research mistake perhaps as it could of been space for another more suitable figure. However being a bare flagpole, the pose can be utilised as a flagbearer for a regular battalion with little modification.
Unless Strelets has found reliable information that indicates they did indeed carry flags into battle.
Perhaps the flagbearer is included because Strelets also has the wargamers in mind. Many rules demand a command set (officer, standard, musician) without regard for historical accuracy. But as Roger said, it can be utilized as a musketeer standard bearer, so not much is lost.