I think what you might be after here could be provided by something in the Lensbaby lineup. This is a series of interchangeable lenses for SLR and mirrorless cameras which have a "lo-fi" look. Particularly, the plastic optic may appeal to you. I'm not sure exactly what you mean by "flatness or shallowness", but you can see some sample photos in the sample gallery or on flickr.
This optic gives a narrower field of view than your cameraphone lens. The Lensbaby plastic optic focal length is roughly 50mm, so on a typical entry or mid-level DSLR, combining it with the Lenbaby Super Wide adapter will give you approximately the same framing you are used to. (The K800i has a field of view of about 50°; depending on the exact sensor size of the camera body you choose, the plastic optic + super wide will be between 45° and 60°. Plus, of course, you'll have the option of not using the adapter to get a longer focal length, in the traditional portrait range.)
Lensbaby produces what they call "lens bodies" to hold various swappable optics, each with a different look. The entry-level "Muse" used to be available for $100 with the plastic optic, but it looks now like they're only selling a $150 pair with the double-glass optic, and then the plastic optic as a $40 add-on. You might enjoy both, so that's not necessarily a bad thing. (You might even want the whole selection of single glass, plastic, and pinhole/zone-plate.)
The lens bodies come in versions for Canon, Nikon, Sony, Pentax (which will also work on Sigma), and Olympus/Panasonic Four Thirds mount. So, you could pair this with any entry-level dSLR, but it's also worth considering the mirrorless options — I think Lensbaby plus Olympus Pen is a pretty sweet setup, and you can get, for example, the EP-2 for under $250.
On the issue of whether you can get exactly the same look, in short, no. Generally, every lens design has a different rendering, regardless of size. Specifically, the small lens and small imaging circle result in a large depth of field, and relatively pronounced limitation on sharpness due to diffraction — roughly like a wide-angle 35mm full-frame lens stopped down to f/22.
Using the Lensbaby plastic optic, dropping in one of the smaller aperture disks should give a similar effect. You'll need to either increase shutter speed to get the right exposure, or — actually — probably both. But one of the advantages of using a larger camera system for lo-fi photography like this is that you get to make more choices about where you want to make those compromises.