For seamless integration with Flex/Flash Builder IDE and SVN use 'subclipse' plugin. Here, http://subclipse.tigris.org/update_1.0.x/, you would find the latest plugin for eclipse.

To install:
Help->Find And Install->Search for new features for install->New remote site
Add Name: subclipse and in URL put http://subclipse.tigris.org/update_1.0.x/

subclipse

To Checkout the project from SVN:
File->New->Other..->SVN->Checkout projects from SVN->
Click "Next" -> Create a New Repository-> Add URL and then select the project folder

There are couple of ways to create branch. But before that one key note.
Say if you are using Tortoise SVN as your desktop client and subclipse as the the eclipse plugin. There could be version conflicts; so do ensure that you make all commits and checkout through subclipse.

Coming back to branching.
Follow these steps from your desktop client for Branching:

1- Create a new folder in SVN for holding branches e.g. "branches"
2- Right Click the folder (trunk) whose branch need to be created
3- Selected "Branch/Tag" option
4- In "To URL" add the location https://foo.com/svn/foosvn/branches/{foobranch}
Note: Don't create {foobranch} folder on SVN beforehand. If you do then you might get an error saying "Path Already Exists".
5- Now select an option the choice e.g."Head Revision",  "Working copy" etc.
6- Click OK
This will create a folder named "foobranch" as a branch of trunk

To Switch to branch:

1- Right click the project folder (which you have checkout from trunk) in the Flex Builder IDE
2- Select Team->Switch..
3- Add the branch URL in "To URL"
Press OK and now your project will be on branch. Any changes that you might have made in your local will now get committed in the branch when you make a commit now.