Nintendo of Australia have confirmed the first big software update for the 3DS will be available in Australia and New Zealand on 7 June:

By performing the free update via a wireless broadband Internet connection, Nintendo 3DS users will have access to an Internet browser and the Nintendo eShop, which will give them access to a variety of new content, including Pokédex™ 3D, an application that lets fans see Pokémon™ characters in 3D.

To celebrate the grand opening of the Nintendo eShop, Nintendo is offering the NES™ game Excitebike™ re-mastered in 3D as a free download until 7 July for anyone who performs the system update. Additional new Virtual Console™ content available with the Nintendo eShop includes Game Boy™ games Super Mario Land™, Alleyway™ and Tennis™. New content is added to the Nintendo eShop every Thursday.

As noted on a few sites, the Japanese website for 3DS was updated recently and the feature list specifically excludes Flash support - so it looks like we can't expect to see Flash support as part of this update.