The first step in scheduling an expedited visa appointment, which I believe you have already done for the brother, is scheduling a regular appointment. The steps after that are outlined on the embassy's website at https://www.ustraveldocs.com/do/en/expedited-appointment/ . They list recommended documentation for a medical emergency appointment, but what you will need to submit will be slightly different. You will need to, of course, document the seriousness of your husband's condition including the very short timeline that you are facing. The other difference will be the documentation of paymment of the medical expenses. You will not need to document how all of the medical bills for your husband will be paid. Rather, you will document how the payment for the visa applicant's (his brother or whoever is applying for the visa) part in the process will be paid, i.e., how the testing and surgery for that individual will be paid by your husband's insurance. It would also be good to provide a little documentation or description of searches that have been done to find a donor already in the US.
The Embassy will also likely want some documentation of the probability that the person seeking the visa will, in fact, be a match. They are not likely to approve a series of expedited appointments for various family members to find a match, for example. I would urge you to investigate all possibilities of getting testing done prior to the visa application to ensure there is the highest probability that a match will be possible. There might be more possibilities for testing in the DR then you're aware of, or there might be a way to get the samples to be tested drawn in the DR and sent to the US for testing. The medical offices dealing with International Services should certainly be able to help you with that information.
I'm sorry you and your family are going through this and wish you the best.