How to flatten this part into sheet metal in Solidworks?

Well, in SW the file you attached is completely useless as far as editing goes. Ok. Here's an example how to create it and the result.
Hope this helps.

Here is a way to do this, using elliptical sketch. It's just roughed out.

Cheers.

I asked. I will answer too.

You can't make a sheet-metal part from oval sketch. It has to be a straight line or a circle - only then you can make it in sheet metal and flatten it.

At least I didn't find any other way.

Try with the attached file (part) SW2010 and try replicating the steps, let me know if you understand the procedure. There are other ways as well, this was the simpler way to explain.

PS. For laser cutting, you will need to do an additional drawing and an additional cut that goes through the radial section under 90 degrees or to do the drawing on the unfolded sheet. Depends on what you want or need.

Brian has the correst solution for sheetmetal
Using sheetmetal loft and normal cuts
This part will flatten
When doing loft increase # of bend lines for better display
Good solution Brian

Look at software packages for the textile/garment/upholstery industry:
www.exactflat.com (Inventor currently, Solidworks version forthcoming)
www.optitex.com (standalone and pricey)

This has a direct application to something I had to work on, which was developing cut patterns for Pontoon Boats.