This is normal. In the beginning stages of the regime, you skin will be fine one day then go mental the next. You can always reduce the amount of BP used if its not tolerable to start with, then very slowly increase the amount. Your skin takes a while before it adjusts to a foreign substance and this is likely what is happening. Its completely normal that your skin may flare up after you apply moisturiser also, however the more gentle you are the less you are going to aggravate your skin. I recommend also try waiting a little longer between applying BP and moisturiser to ensure your skin has time to absorb and settle before the next application. Also if you are experiencing burning in the mornings it may be best to do the regime first thing in order to give your skin time to settle before heading out.
Be consistent, follow the steps very carefully and your skin will respond. All the best.