Down Syndrome is a human disorder in which there's a wrong number of chromosomes (trisomy 21 -- three sets of the 21st chromosome instead of two, totaling 47 chromosomes instead of 46). Other animals do not have Down Syndrome due to this specific definition; they can have their own mutations that yield outcomes similar to human Down Syndrome though (source). That said, this daisy does not have Down Syndrome since it's not possible. This phenomenon is called fasciation, which can be due to genetic mutations or environmental factors (source).