This is a reasonable map of the period when the HYW began - you can see the problem with “Italy”.
http://historymedren.about.com/library/atlas/natmapeur1346.htm
You could reasonably use Castille for Spain, i.e
http://en.wikipedia.org/wiki/File:Castile_Arms.svg
Denmark:
http://en.wikipedia.org/wiki/File:COA_of_Denmark.svg
(use yellow instead of the rather silly “gold”.)
Germany (HRE):
http://en.wikipedia.org/wiki/File:Holy_Roman_Empire_Arms-single_head.svg
(note the Eagle became double-headed after 1368)
Russia at this time was a host of petty kingdoms; but the genesis of the Russian state lay in the Rulers of Muscovy whose arms were:
http://en.wikipedia.org/wiki/File:Coat_of_Arms_of_Moscow.svg
or if you prefer Kiev take your pick of these:
http://commons.wikimedia.org/wiki/Category:Coats_of_arms_of_Kievan_Rus
Hungary, House of Arpad is barry of 8 gules and argent:
http://en.wikipedia.org/wiki/File:Hungary_Arms.svg
As for “Latin Empire”; this is presumably the late Byzantines, barely clinging on to Constantinople:
http://en.wikipedia.org/wiki/File:Palaiologos-Dynasty-Eagle.svg
In the game officially (as it’s in an earlier period) this may refer to the Crusader Empire:
http://en.wikipedia.org/wiki/Latin_Empire
For Italy maybe the Kingdom of Sicily, but this was a variant on the Aragonese arms since Sicily was ruled by a junior branch of Aragon:
http://en.wikipedia.org/wiki/File:Aragon-Sicily_Arms.svg
Charles of Anjou founded the Kingdom of Naples, but the arms were again those of a junior branch, this time of the French house. He later impaled these with the arms of Jerusalem to form this:
http://en.wikipedia.org/wiki/File:Armoiries_Anjou_Jérusalem.svg
But it really isn’t remotely Italian.
Lastly you might consider the arms of Savoy, whose Duke founded the modern Kingdom of Italy:
http://en.wikipedia.org/wiki/File:Blason_duche_fr_Savoie.svg
Bear in mind that there is a difference between “national” flags and the “arms” of the Kingdom; for example the FLAG of England is the Saint George Cross, while the ARMS of the Kingdom of England are the 3 gold lions on red (though in fact they’re actually derived from the lions on the arms of Normandy, Aquitaine and Anjou from where the medieval Kings of England originated, so they are really French lions.)
Edit:
Do you know what the figs you intend to use are, or are there pics of them anywhere?
I might be able to do some flags for the Warlord pieces to match the shieldels, or maybe to fly from the castle tops.