Command Accountability for Military Family Readiness Act This bill requires each military department to prioritize military readiness. Specifically, each department must designate the command personnel who shall undergo a climate assessment that takes into account their support of military family readiness; provide training, guidance, and other information to ensure that such command personnel are equipped to encourage and support military family readiness within their unit or installation; ensure that each assessment includes the extent to which the command personnel encourage and support military family readiness; and ensure that each assessment includes surveys of the spouses of service members on matters that are relevant to military spouses, military families, and military family readiness.