No, it is not Fratelli Toso. Toso millefiori pieces have depth to the canes. Toso workers fit the canes together in a way that there was no room left between the canes, though there are exceptions. Usually the canes were satinized, though again there are exceptions. Handles of the millefiori vases were usually made of multicolor canes or satinized clear glass. Toso pieces tend to look and feel smooth and chalky. The base will have "runny" canes on the bottom that were probably made from canes that were tangentially cut. (Leslie Pina's book Fratelli Toso is excellent for learning the look of Toso pieces. I recommend it to anyone interested in investing in millefiori. The book will pay for itself quickly in helping to pick only the best pieces.)
Your vase is a very nice one. I have seen it before, but cannot think of who makes them. I'll have to go through my catalogs again to see if I can locate the design.