I own a studio of 2D artists and I'm thinking of creating a 2D browser-based multiplayer game development division and start with a simple game the likes of Urban Rivals (www.urban-rivals.com). What kind of programmers or what skills should I be looking for in a programmer for this kind of project? Should we use Flash?

Use Flash only if the design/gameplay of your game requires it!

Otherwise, look for Web Developers/Programmers with knowledge of a web/scripting language such as PHP, Java (jsp), ASP, Python and so on. In theory you could go the CGI route and use basically any programming laguage.

I would imagine you would also need a DBA and somebody able to design your database schema too.

Really there are so many ways to develop for the web it comes down to experience/track record of your programmers.

For a good example of what can be done, have a look at what is already created. There are many games that are made in Flash, many are made in Java using their 3D API. There are even some which are based on normal postback HTTP methods. Have a hunt and see what you can see.