If you are the spouse of a service member stationed in Hawaii and neither of you is a Hawaii resident, the income you earn in Hawaii can be exempt from Hawaii income tax.
There is nothing to file with the Office of Veterans’ Services. Claim the exemption on your Hawaii return, and give your employer your out-of-state residency information so Hawaii tax is not withheld. Hawaii Department of Taxation Tax Information Releases 2010-01 and 2019-01 set out the rules.
Your service member’s orders assigning them to Hawaii, proof that you and your service member are residents of another state or territory, and your marriage certificate.