If I upload a game to DimeRocker to create a facebook game with it, will someone like Shockwave or BigFish still accept it into their portal, or is it like book publishing where you have to pick a single publisher?
No. Both shockwave and Bigfish are ok with getting non-exclusive content. Shockwave offers non-exclusive (25%) and exclusive deals where the latter one gets 35% from the rev share (which usually is not worth considering from my experience).
As developer it is the best deal to license out your game to multiple channels. More or less the only way to recoup the development costs these days. Checkout also http://www.gamecot.com/ to offer your game to multiple publishers.
It looks like DR does not impose restrictions on your project. At least no information about it in license FAQ.
You might want to check the portals linked in Which game portal websites accept Unity webplayers?. You should be able to find the information you are looking for in their terms for developers.
It looks like there are two models for most publishers, exclusive and non-exclusive. Exclusive seems to get more benefits. A couple of samples:
http://www.kongregate.com/pages/earn
By default, all developers receive 25% of the ad revenue generated from their games. This includes all ads within the games and any potential ads on the game page that may be added in the future. Games that are integrated with Kongregates Statistics & Challenges API earn an additional 10%, and games that are offered exclusively on Kongregates site earn an additional 15% (see below). Thus, its possible for a game to earn 25%, 35%, 40%, or 50% of ad revenue.
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To qualify for an additional 15% of your games ad revenue, the game cannot be hosted on any website beyond Kongregate.com, with the exception of your own personal site.
http://www.shockwave.com/about/developers.jsp
Content which is hosted exclusively on Shockwave is even more lucrative than non-exclusive content but we provide competitive rates for all content.