There's no evidence that they did, mate. Unlike the Prussians the Austro-Hungarians (and many other armies) created ad hoc grenadier battalions as required, by taking grenadier companies from line battalions as required- which you probably already knew. No contemporary artwork or accounts I know of show or mention them having colours, not that that is conclusive evidence. As far as I know they weren't forbidden to carry colours, as were the Prussians before 1807, so they may have done so.Didn't real Austrian grenadiers actually have flags?
For my little white metal representations, though, I get to decide what they carry.