Dear Samantha,
You can obtain a "home kit" for taking DNA samples, and if your brother is eligible for contact visits may be able to arrange with the jail to take the sample. This is now typically done by cheek swab. You should check with the jail before ordering the test, as if they won't let you take a sample then buying the test kit while your brother is incarcerated would be a waste of your money.
However, given that you would also need a sample from the baby, you may be better served by waiting for the court-ordered test to be performed.

