Can a PDF contain something that tracks you?
Generally PDF DRM/tracking is done as combination of a PDF with proprietary data in it, combined with specific PDF reader to interpret that data.
can it contain a remote image that, when the PDF is opened, will fetch that image
No, PDF does not support external images in the page content. You can have references to external resources, but these have nothing to do with displaying the PDF, and in general a PDF reader would not fetch that remote resource automatically, though a particular PDF reader application could do that.
Or maybe embedded Flash?
Same as above, but I believe only Adobe products would do this. Would be a much smaller set of PDF readers that would have built-in flash support.
I can imagine this might exist if the user clicks through a warning, but can a PDF do this without triggering a warning to the user?