Can I claim expenses incurred while campaigning for a union elected position at work? (For example, printed flyers, banners, signs, pamphlets, t-shirts)

No. These are not deductible as business or personal expenses. 

You can still deduct your union dues, but not expenses of a campaign involving the union.

For more information on qualified business expenses, please follow this link: https://www.irs.gov/taxtopics/tc511