There weren't really that many Finnish Regiments in service at the time. In 1809 Finland was given leave from providing any armed forces for the Russians to let them recover from the war of 1808. 3 Regiments were raised on a voluntary basis for 1812 and at least officially were intact until 1830. 2 were Line Regiments and 1 a Jäger regiment and all were transformed into Sharpshooter units in 1827 and disbanded in 1830. The Finnish Guard was promoted from the training battalion based in Helsinki in 1829 and served until 1905 and fought in Poland in 1831.
For your period I wouldn't really say that there was any other purely Finnish unit than the Guard. Recruitment into the others was stopped in 1827 and even before that they hadn't been very active. There were of course quite a few Finnish officers and soldiers in service in other Russian units, but no Finnish Regiments were active outside of the Guard.
The Finnish Guard uniform in 1830.
And the flag after 1831.