Landlord Accountability Act of 2019 This bill provides protections to tenants of certain federally assisted housing and establishes a low-income housing maintenance tax credit for eligible landlords. Specifically, the bill prohibits discrimination, in the context of rental housing, against individuals who possess a housing choice voucher. Additionally, landlords may not take, or fail to take, certain actions with the intent to make a unit ineligible to receive assistance from the Department of Housing and Urban Development (HUD). Landlords that violate this prohibition shall be fined by HUD for each violation and may be sued by tenants who are harmed. In addition, the bill allows HUD to provide grants to states, Indian tribes, local governments, and affordable housing organizations to develop, expand, and assist tenant harassment prevention programs. The bill also provides protections to tenants of multifamily housing projects by requiring HUD to (1) increase the staffing level for the Multifamily Housing Complaint Line, (2) create a Multifamily Housing Complaint Resolution Program, and (3) publicly disclose on its website information regarding each complaint received under the program. Landlords must also display in certain multifamily housing projects information about the complaint line and the phone number of the regional or local HUD office. In addition, the bill provides a tax credit to qualifying landlords that is equal to the landlord's low-income housing maintenance expenses for the year. To qualify, landlords must have addressed within 30 days any complaints filed against them under the complaint resolution program.