To be honest, most fibrous mangoes do not have the greatest of flavor. Probably the best would be the Peach Turpentine (which actually hase really good flazvor) though not sure where to purchase one. Madame Frances - blech flavor wise; East Indian - blech flavor wise; Tommy Atkins - do I really need to comment ?
Actually, I have to disagree. There are many fibrous mangoes that have great flavor. I heard Gary Zill and Maurice Kong argue that the best flavor, most intense mango taste came from the lower portion of a fully ripened East Indian Mango. Not the upper portion mind you....just the lower portion....LOL. Anyway, I have a seedling tree that I planted from a Mallika seed which came from a Mallika mango I had at Four Fillies Farm back when Crafton Clift was working there. The tree has about 7 or 8 years of fruiting and is very different than its parent, Mallika. It has lots of fiber, but also has the most intensely pleasant mango flavor that I have encountered. For those that can't do fiber, you won't be happy with this fruit. But for those that can tolerate some fiber if the flavor is really good, this could be for you. I have served it on many a tasting table and it always gets a "Wow, what an intense flavor!" Of course I have no trees propagated......just in case you are going to ask. But I have had requests for budwood. This year, like its parent Mallika, the crop is very, very light.