Lets say hypothetically somebody with klinefelter's actually manages to have a child with their partner, is there a risk of the child inheriting klinefelter's and if so, what is the likelihood?

Klinefelter syndrome is not inherited; the extra X chromosome occurs during the formation of eggs or sperm in one of person's parents. During cell division, an error prevents X chromosomes from being distributed normally among reproductive cells as they form. Mosaic Klinefelter syndrome (46,XY/47,XXY) is also not inherited. It occurs as a random error during cell division during fetal development.

These rarely occur and are often only possible with the aid of a fertility center and specialized "test tube" fertilization. Sperm are extracted from the male and injected into eggs. Unfortunately many embryos that result have abnormal numbers of sex chromosomes or autosomes 18 or21. I would consider random natural pregnancy unlikely & outcome unpredictable. There is just not enough data to know.