Are there any races that are genetically linked to downs syndrome?

No: Down sydrome occurs in all races and all ethnic groups at about the same rate. It is probably impossible to truly compare occurence rates in various groups because of the many inter-racial or inter-ethnic families in america. A study done about 20 years ago reported that hispanic women had a slightly higher rate of Down syndrome babies, but I am not sure how valid those study results are.

Not really: Doctors use epidemiology (population analysis) to determine prevalence rates of diseases & conditions. The rate of down's is about 1.53 per 1000 pregnancies. Maternal age is the most important risk factor for ds. But hispanics under 40 were more likely to have ds, & pacific rim islanders more than filipinos, far asians, europeans or africans. Authorsbishop j, et al. Journal am j epidemiol. 1997.