The postproduction workflow with the BMPCC depends a lot on the settings with which you shot your material. Unless you shoot in the Video-Mode, you need to do some adjustments to the image to make it look visually pleasing. This can be done either before you start editing by creating color graded copies of your original clips (proxies), during editing (by applying color correction in the editing program), or after editing in a color grading step.
Dynamic Range “Video”
You can actually get “usable” footage directly off the camera if you set the dynamic range to “Video” and record in any of the ProRes settings. This will apply a Rec.709 lookup table in the camera, while reducing the dynamic range of the camera. While this is possible, most people would probably want to choose one of the other options which take advantage of the the sensors full dynamic range. Additionally the Rec709 LUT applies often non-satisfactory look (colors, contrast) to the material.
Dynamic Range “Film” - ProRes
If you are interested in the Data-Rates and characteristics of the different ProRes settings, check out the Apple Whitepaper on Prores. And Here is a good introduction what LogC recording means, this is from the Arri Alexa but the principle is the same for the BMPCC.
The Material that comes out with “FILM” setting from the BMPCC needs to be Postprocessed, since it lacks contrast, gamma and saturation. There are several ways to do so, the easiest to apply a ready made LookUp Table (LUT). This can be done either in a color grading software like Blackmagics Davinci Resolve or in your favourite editing software directly. Applying a LUT can be compared to what selecting a preset with “normal” video cameras was.
Dynamic Range “Film” - RAW
Recording RAW images in general means that the image of the sensor is read out without any camera-internal manipulation. Each of the Images is stored as a single (lossless compressed) DNG Image file which contains the image data plus the Camera Settings you used during shooting - but only as meta data. So if you set a White Balance while shooting in Raw-Mode, this is not directly applied in-camera but will be in the process of “developing” the digital negative. The advantage of raw files is a 12-Bit Color depth compared to 10-Bit in Prores, the disadvantage is a huge volumes of data being recorded. This means that you need a very fast SD-Card and the according setup to transfer, store and backup this data.
We also have a section on open source tools for video and audio conversion and manipulation, with some scripts that might be useful for your workflow: FFMpeg Conversion Workflows