What is the usual pattern of cash flows for a share of preferred stock? How does the market determine the value of a share of preferred stock, given these promised cash flows?

Preferred stock has no maturity date thus it has no maturity value.  Future cash payments of preferred stock are dividend payments that are paid to preferred stockholders at regular time intervals for as long as they (or their heirs) own the stock.  Cash payments as of preferred stock dividends are scheduled to carry on forever.  To value preferred stock we adapt the discounted cash flow model to imitate that preferred stock dividends are perpetuity.