This is what I have learned from various history books.
I am not a historian, but I did my best, and believe this
to be correct.
The original coat of arms used by the first Premyslid prince was
a Flame Eagle (the Saint Wenceslas Eagle) derived from the eagle
of the Holy Roman Empire. The first Premyslids, as imperial princes,
also had the privilege of using a red standard. This followed from
the obligations of the Czech sovereigns towards the imperial
throne.
In the 1200's, as the power and prestige of the Premyslid kings
grew, they adopted a more imposing symbol of a lion. It was placed
on the original red standard. It had two tails to be a supernatural
animal, a crown to express the sovereignty of the kingdom, and its
white colour was once again derived from imperial symbolic.
This royal coat of arms, also placed on a gothic shield, came to
symbolize the land of Bohemia too, as well as the entire Czech state.
Incidentally, the vacated Saint Wenceslas Eagle was adopted, and is
still used, by some Italian city or region.
Sometime in the 1700's, national flags were created all over Europe
in a fairly standardized way: the colours of the coat of arms were
placed on a flag in stripes. So the Czech national flag was a white
stripe over a red stripe.
In 1918, when Czechoslovakia was created, the flag turned out to
be the same as Polish. The parliament decided to add a new colour
to avoid confusion, and to express the new quality of the state
with Slovakia included. The colour chosen was blue, because it
appeared in the Moravian and Slovak coats of arms, and also the
three colours would form the Slavic tricolora. A third stripe would
have caused confusion with some other European flags, so a wedge
was chosen as one of the oldest Czech heraldic figures.
The coat of arms had a large, medium and small forms, the large
one including all the Czechoslovak lands, such as Moravia, Silezia,
Slovakia, Ruthenia...
After the split of Czechoslovakia, the Czech Republic retained
the flag, and formed a new large coat of arms containg the Czech
lion, the Moravian eagle (chequered) and the Silezian eagle
(black in gold). The shield is divided in four fields according
to heraldic rules. The small coat of arms is only the lion.
The nice thing to say about Czech symbols is that they are very
much historical and strictly heraldic, and that the Czech flag
is among the few noble European flags whose white and red
came from the colours of the Holy Roman Empire (together with
Danish, Austrian and Swiss flags).