How could tree rings from bristlecone pines support the theory that some areas have had periods of drought and flooding for hundreds of years

They can't

Explanation:

Why? *heh* I though you'd never ask. As they grow from season to season, coral reefs in the oceans and trees on the land both hold small different aspects in the climate. These recorded details can tell scientists about growing conditions in the oceans or on the land, but the record only grows across the collective lifetimes of the organisms that have been protected through the years. Thus, even though their records are more detailed, reefs and trees cannot provide records that are as long or ever-so-lasting as ice or sediment core records.