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I think I have just found the answer to my question and confusion. "Where did the Flats comes from?", was my question. The answer can be found in Quick Tip, "How to Improvise Piano With th Dorian Scale.
C-Dorian as used in this case is simply the first note of the scale you are looking at. Actually, "C" is the SECOND NOTE OF THE (Bb Major Scale and would be called the Dorian scale starting with the second note of the Major Scale. Or, in this case. Note "C''. The diatonic structure of Bb Major requires 1/2 tones between notes 3-4, and 7-8 just like any other Major Scale. Thus it produces note b4 and b8, or Eb and Bb. Now if we start on the second note, we get C - D - Eb - F - G - A - Bb. That is the Dorian Scale of Bb Major. Now I'm getting somewhere. Thanks Peter, you've been helpful.