To "dominate a battlefield" just means to beat it, you don't have to find all flags or do anything special. Just beat the level and it counts as "dominated".
There are 46 total main and sub battlefields, with additional sub battlefields unlocking continuously along the way. There will also eventually be a few in the village area which might be easy to miss.
You can check your progress under the Title "Ruler of the Crouching dragon" under "Fame of Expert" which will tell you how many you've done.