What is the common pattern of cash flows for a share of preferred stock? How does the market define the value of a share of preferred stock, specified these promised cash flows?

Preferred stock comprises no maturity date, thus it has no maturity value.  Its future cash payments are dividend payments which are paid to preferred stockholders at regular time intervals for as much as they (or their heirs) own the stock.  From preferred stock dividends the Cash payments are scheduled to continue forever. To value preferred stock, we get used to the discounted cash flow model to reflect that preferred stock dividends are perpetuity.