No, I find nothing in the Bible that would prevent you from offering one of your kidneys to your brother. His doctors would, of course, need to be sure it was medically possible, but you shouldn't worry about it from the Bible's standpoint.
In fact, I commend you for your willingness to do this. Often today, people are asked (perhaps when renewing their driver's license) if they're willing to be organ donors when they die -- and I encourage people to do this, if their family agrees or there isn't any other barrier. Countless thousands today are alive because of blood transfusions, and I'm always thankful when I see a sign outside a church advertising a blood drive. What you're considering is similar to these efforts.
I couldn't help but think of Jesus' familiar parable about the Good Samaritan (you will find it in Luke 10). You probably know the story: A man was robbed on a lonely road and left for dead, and the first people who came by ignored him. Finally, a Samaritan stopped, tended the man's wounds, put him on his donkey, and took him to an inn where he could recover -- at the Samaritan's expense.
It may be costly to help those in need (like your brother), but God calls us to do all we can to assist them. After all, Christ didn't abandon us, but gave His life for our salvation. "Dear friends, since God so loved us, we also ought to love one another" (1 John 4:11).