Usually when we talk about genetic disorder risks for closely related pairings, the concern is the high probability of homozygous recessive alleles.
Lazarin et al. 2013 screened ~23,000 individuals for 108 genetic diseases and found 24% were carriers of a known allele for some disease. Including carriers of multiple alleles, the total frequency comes to about 38% (this is a lower bound because only known alleles can be screened; there may be many other variants that are not known to science that cause the same symptoms).
That means about a 62% chance that one of an individual's parents carries one of these alleles (1-.62*.62 - note that this 62% has nothing to do with 1-.38, just a mathematical coinicidence with rounding).
If a parent is a carrier, each sibling would have a 50% chance of also becoming a carrier; the probability that both siblings are carriers would be 25%. The probability that an offspring from those siblings would be homozygous recessive would be another 25%. .62*.25*.25=3.9% (note that these are all lower bounds, the chances would be much higher if there were multiple recessive alleles present or if both parents were carriers for the same gene).
However, this is limited to Mendelian mutations just for this subset of known alleles. There are many many more conditions and disorders that have more complicated genetics that we may or may not understand, so that the original question becomes nearly unanswerable. In fact the paper I cited only paid attention to what were considered "major" disorders and even left out the Mendelian alleles known to cause more minor issues (including clotting disorders that can easily lead to death in the right circumstances). There are also many mutations that don't cause a clearly defined disorder but cause some other more limited issues that could predispose the offspring to other illnesses.
Lazarin et al. 2013 refers to estimates that each individual carries about 4-5 lethal recessive mutations. Given that siblings are very likely to be carriers of the same particular recessive mutations, this would significantly impact any offspring well beyond the estimates for the known disease alleles.
Lazarin, G. A., Haque, I. S., Nazareth, S., Iori, K., Patterson, A. S., Jacobson, J. L., ... & Srinivasan, B. S. (2012). An empirical estimate of carrier frequencies for 400+ causal Mendelian variants: results from an ethnically diverse clinical sample of 23,453 individuals. Genetics in Medicine, 15(3), 178-186.