Horizontal black-white-red with a thin yellow horizontal stripe on the middle of the white.
According to the company website, Companhia Aliança de Navegação was founded in 1951 by a German immigrant named Carl Fischer, who had arrived in Brazil in 1928 and entered the fruit business. Aliança was originally limited to coastal trade, since Lloyd Brasileiro, the government-owned line, had a legal monopoly over the transoceanic traffic. Aliança was allowed to enter the foreign trade in 1967 and now serves Europe, the U.S. east coast, the Caribbean and Gulf of Mexico, and both coasts of South America. It has 5 vessels totaling 178,000 deadweight tons, employs 283 people, and had revenues of US $180,000,000 in 1999. I would speculate that Fischer's German origins would account for the black-white-red horizontal tricolor that serves as the field of the house flag.
S.A. Loughran (1979) confirms that the colors represent the origin of the company founder with the interlocking rings standing for the two hemispheres. The company itself, or its assets and brand, were acquired by Hamburg Süd in 1998, originally being placed under Aliança Transportes Maritimos S.A. which changed name in 2000 to the current Aliança Navegação e Logistica Ltd. Lloyds give it as a new company formed 1998 but the website, which is the old one, originally showed the history of the original company but no longer does - so the exact connection is unclear. What is clear is that Hamburg Süd acquired the brand including the livery and have continued to use this unlike their other takeovers which after a few years were incorporated into the group Hamburg Süd brand.
However the "current version" flag of the black, white, yellow and red unequal horizontal multibands which Dov has taken from the company website, to which the link still works, is from a flag-like section of the main logo appearing on the welcome page. This at best gives it a "maybe" rating for me and an unlikely one at that, failing better evidence, due to their company page having a photo of the 1993 flag flying from a ship which I would take as indicative that like the funnel markings, the 1993 flag is still used. The yellow rings are hardly visible but under a magnifier they can be made out.