401(Kids) Education Savings Account Act of 2014 - Amends the Internal Revenue Code to: (1) eliminate after 2014 the income-based reduction of contributions to Coverdell education savings accounts, (2) increase the annual contribution limit for such accounts, (3) allow the use of such an account to pay home school expenses and the acquisition costs of a first-time homebuyer, and (4) allow tax-free rollovers of amounts in a Coverdell education savings account to a Roth individual retirement account (Roth IRA).