First question: are you planning on using your Photoshop created screen files, to cover the ENTIRE screen width/height of your Flash Builder project? For example, a screen image set up for a Motorola Droid would need to be 480px wide X 854 px high....vs.....say a Samsung Galaxy S3 screen of 1280px X 720px. In each case, you will need to use the multi-dpi image settings to compensate for the variety of image screens (backgrounds) that you will need. I myself have extensive knowledge in this area, as most of my applications include heavily creative PSD graphics.
So to begin, you will want to create a source folder to hold your images (screens). You do this by "right clicking" on the "src" file of your newly created mobile app project, and creating a new "Folder" called simply..."assets". Once completed, your new "assets" folder will appear in the "src/source" folder. Now, open Design View in Flash Builder...and drag an "image" component from the tray on the left...and place it on your app screen. Constrain the top, bottom, left, and right of the image component to 0, if the dimensions of your PSD/.png graphic file are say...480 x 854. This will set your image to fill the whole app screen. Next, we'll drag our graphic from Photoshop...and drop it into our newly created "assets" file. After this, and while still in design mode, we'll set the source of the image, to the image we just placed into our "assets" folder. Once that is done, click the refresh icon on the tool bar above Design Mode....and your new background will appear in your Flash Builder project.
Of course, if you are going to use multi-dpi images for backgrounds, then we have a few more steps to cover beyond this one.
Hope this helps you,
Software Architect | SwitcHHat.com
You can import them in Flash Catalyst and then export the project from Flash Catalyst to Flash Builder.