Does it handle promotion-driven demand spikes (BFCM, flash sales)?

Partly, with help from you. Prophet has first-class holiday support, so recurring promotions (Black Friday, Cyber Monday, Boxing Day, Diwali, EOFY) are easy: add them to the holidays DataFrame with appropriate lower_window and upper_window values to capture the lead-up + tail. Ad-hoc flash sales are harder: treat them as a custom regressor with a binary on/off flag per day, and include the regressor in future only for planned upcoming promos. Critical: don’t let flash-sale spikes corrupt the baseline, either tag them as holidays or use Prophet’s outliers support to mark them as exceptional days the model should ignore for trend.