What will happen if two taxpayers claim the same child, the IRS will flag both returns and ask for proof of the taxpayer's claim.

Since your son does not live with his father, he's not going to be able to claim the child unless he can produce a form 8332, signed by you allowing him to claim him. You can see this form here: http://www.irs.gov/pub/irs-pdf/f8332.pdf

Do you and your child live with your mother? If so, she will have no problem claiming not only your child, but you as well since you have no income.

If you do not live with her, it can get a bit sticky. If you are receiving subsidized housing, food stamps, medicaid, etc, the value of all of that is counted towards supporting your son along with child support. Your mother will need to prove that she herself is providing more than half of the child's support. It's possible that no one can claim your child if public aid is providing the majority of his needs and the custodial parent does not work.

If the child doesn't live with her she can't use your child for certain tax credits if she is providing more than half of his support: The earned income credit, is the big one.