You can take both Advair and Prednisone together. I agree that you should be working with your doctor.
My asthma plan that I put into place with my Pulmonologist includes both.
I'm currently taking Advair 250/50. When I have a bad flare, I use my Albuterol and go up to Advair 500/50 for a while. If I have signs of an infection, I'm to take an antibiotic. If the flare is really bad, I take a tapering dose of Prednisone.
I do monitor my peak flow throughout. However, I tend to to better just by knowing my body because the peak flow doesn't always reflect how I'm feeling with my asthma.
Through monitoring me closely, my Pulmonologist has gotten to know how I do monitoring my own asthma and how well I'm doing at treating my asthma. I now have a standing prescription for the Advair 500/50, antibiotics and the Prednisone. My written asthma plan hangs on the side of my fridge so I have it handy as a reference to follow.