Roth IRA Flexibility Act of 2013 - Amends part B (Supplementary Medical Insurance) of title XVIII (Medicare) of the Social Security Act with respect to the formula for reductions in the income-based subsidy for premiums under Medicare parts B and D (Voluntary Prescription Drug Benefit Program). Disregards, in computing adjusted gross income in that formula, any amounts transferred from a traditional individual retirement account (IRA) to a Roth IRA.

Amends the Internal Revenue Code to authorize the use of tax return information involving such amounts for disclosure to carry out those subsidy adjustments.

Directs the Secretary of Health and Human Services (HHS), in collaboration with the Commissioner of Social Security, to refund to an individual the portion of premiums paid under Medicare parts B and D equal to the difference between the premiums paid and the premiums the individual would have paid if any rollovers to a Roth IRA from an eligible non-Roth IRA retirement plan made on or after January 1, 2011, had not been taken into account.