In order to deduct the contribution, the veterans' group has to be authorized by the IRS to accept tax-deductible contributions. Ask them if they have a "determination letter" from the IRS, or look up the group using the Search for Tax Exempt Organizations on the IRS web site.
Donations to charity are an itemized deduction. They will not reduce your tax or increase your refund unless your total itemized deductions are more than your standard deduction.
