Hi Jay
As you probably already know, Russian flags were very similar to the Prussian style. The basic design consists of a central eagle and wreath device, crowned cyphers at each corner and a cross. Variation was provided by the use of different colors and divisions of the cross and/or corners.
In 1797 Czar Paul I authorized new patterns for the army's flags and during the next 2 years each regiment received 1 "white" flag, corresponding with the Austrian or Prussian "Leibfahne" or British "King's Colour", and 1 "coloured" flag per company, corresponding to the battalion or regimental flag of the other nations.
In 1797 the Arkangel Regt - which was in the future Lithuania Inspection - had a "white" flag that had a white cross and green/brown corners and a "coloured' flag that had a green cross and brown corners.
In 1800 Czar Paul I replaced the divisional organization of his army with military districts called Inspections, and authorized new flags in the Inspection colors. However very few of these flags were issued and most regiments continued flying the 1797 flag.
Arkangel received it's new standards on 28/2/1800. Other regiment known to have received the 1800 flag were Moscow and Siberia on 6/3/1800, Smolensk on 7/3/1800, Tauride on 30/3/1800 and the newly raised Lithuania on 2/4/1800 and Kabardinsk on 17/12 1800.
Of the new regiments raised by Paul it appears that the earliest most of them received the new flag was 1805.
The 1800 pattern was carried on staves with a gilt spear tip type finial and the stave colors seem to have been used as a means of identifying regiments within the Inspections.
The Lithuania Inspection 's flags were "white" flag - white cross with red/black corners and a "coloured' flag - black cross and red corners.
Each Regiment got 1 "white" flag and 9 "coloured" flags
Hope this helps some.
:cheers;
Larry
My source is :
Osprey Men at Arms series Flags of the Napoleonic wars (2) Colours, Standard and Guidons of Austria, Britain, Prussia & Russia.