I am in the 15% tax bracket so my capital gains from mutual funds are tax free. Should I reinvest them in the fund or withdraw the gains and invest them in a Roth IRA?
The source of the $'s you are putting into an IRA is not important. The IRS only cares about having income and does the amount allow you to make a deductible contribution to an IRA, or a contribution to a Roth IRA.
So assuming that you have income this year, and that it is not too large to contribute to a Roth IRA. Then you need to decide if you want to contribute to a Roth IRA and how much you want that to be.
The mechanism is not important. Some people make a monthly contribution. Others wait to the end of the year, or even for their tax refund (because the last day to contribute to an IRA is the end of the tax season). Others when they get a bonus, or with their birthday checks. They choose the method that maximizes their chances of not missing the money.
If the taxable mutual fund is in the same fund family as the Roth IRA it may be easy to have it automatically moved to the Roth. But if that is not the case your plan will still work.
Only you can decide what mix of 401K, IRA, and taxable investments you need to make this year. The actual moves you need to make to achieve that goal is not important. Your plan is essentially a way to rebalance your investment mix from taxable to non-taxable. If it meets your goals, then go ahead.