Jobs and Childcare for Military Families Act of 2021 This bill allows an employer a work opportunity tax credit for hiring the spouse or domestic partner of a member of the Armed Forces and requires the creation of programs for service members to pay for childcare on a pretax basis. Specifically, an employer may receive a tax credit equal to 40% of a new employee's first-year wages if the employer hires a service member's spouse or domestic partner (as recognized under state law or by the Armed Forces). Currently, a similar tax credit exists for employers who hire certain disadvantaged individuals, including disadvantaged veterans. The Department of Defense and the Department of Homeland Security (with respect to the Coast Guard) must implement flexible spending arrangements that permit members of the Armed Forces to use basic pay and compensation to pay on a pretax basis for dependent childcare.