You have covered in several previous posts the question of whether contributions made in support of mission trips are deductible. Here's a question with a slightly different slant.
If a congregation member, who is a member of a mission team and travels with that team, purchases supplies, food, or other “goods” for the trip and those supplies are used directly and immediately for the purpose of the trip (in other words, they do not run those contributions through the church), will that person be able to deduct those as contributions, assuming they have supporting documentation? Will they have to get some kind of statement from the church in support of those contributions? Would they claim these on Schedule A, assuming they itemize?
IRS Publication 526 offers some good help to answer this question.
"Although you cannot deduct the value of your services given to a qualified organization, you may be able to deduct some amounts you pay in giving services to a qualified organization.
The amounts must be 1) Unreimbursed, 2) Directly connected with the services, 3) Expenses you had only because of the services you gave, and 4) Not personal, living, or family expenses."
The Publication has a good section on travel expenses, plus a table of Volunteer's Q&A. It includes a summary of deductible travel expenses. "These include 1) Air, rail, and bus transportation, 2) Out-of-pocket expenses for your car, 3) Taxi fares or other costs of transportation between the airport or station and your hotel, 4) Lodging costs, and 5) The cost of meals. Because these travel expenses are not business-related, they are not subject to the same limits as business related expenses."
So in answer to the questions above, "yes," with proper documentation the costs for volunteers' travel expenses can be deductible.
In the event of an audit, the taxpayer may need proof from the church that volunteers were involved in a charitable activity that involved paying their own costs in giving services (to use Publication 526 language). Absent an audit, such proof is not necessary.
Volunteers' costs are deducted along with other contributions on Form 1040, Schedule A.