More info on the new currency exchanges in Burma: There is now a bank-run currency exchange at the airport in Yangon. Reports have varied a bit, but it appears that the exchange rate used is close to the old “black market” rate.

In the city, the bank-run exchanges have recently had the best rates, about 10 kyat per dollar more than the black market rates. So far, such bank-run exchanges only exist in Yangon. There have been long lines of locals trying to exchange dollars for kyat. Recent exchange rates have been around 800 kyat to the dollar. Typically, exchanges set their rates twice a day.

These bank-run exchanges will exchange not only dollars, but also Euros and Singapore dollars. 
 However, this has not eliminated the need for crisp, unmarked US dollars. You still need US dollars to pay for hotels, flights, and admission fees.