How often is 羊肉 Goat in chinese?
In English, 'lamb' is meat from young sheep and 'mutton' is meat from adult sheep.

Young goat meat in Chinese is '小羊肉'  (a goat under a year old).
Adult goat meat in Chinese is  '山羊肉' or simply '羊肉'.

Goat meat is commonly consumed by Chinese, but far less than pork and beef.

How often is 羊肉 goat in Chinese and not mutton?

The term '羊肉' always refers to 'goat meat' in China. 'Mutton' is translated as 绵羊肉 and 'lamb' is translated as 羔羊肉. Almost no one eats them in China.
Since most of China has no sheep, the terms 'lamb' and 'mutton' in China are  adopted to describe 'young goat meat' and 'goat meat' respectively.
Simply put, 'lamb' and 'mutton' in Chinese should be 羔羊肉 and 绵羊肉, but most Chinese think 'lamb' and 'mutton' mean '小羊肉(young goat meat)' and '山羊肉(goat meat)'.
Edit:

History of the_domestic sheep https://en.wikipedia.org/wiki/History_of_the_domestic_sheep
Sheep are not an important part of China's agricultural economy, since the majority of China does not have the large open pastures required for sheep-rearing.[20] Sheep farming is more common in the northwestern provinces of the country, where such tracts of land exist.[21] China does have a native sheep breed, the zhan. The population of the breed has been in decline since 1985, despite government promotion of the breed.[22]

Since China is quite hilly, sheep farming mostly confined to the minorities tribes in northern edge of the country. A typical Han Chinese might not had seen a sheep in his entire life.

China’s Goat Industry: http://www.ccagr.com/content/view/115/179/
China is home to more than 100 million meat goats. Farmers produce a total output of more than 1.5 million tons annually. Most of the meat produced is consumed by the nation while little is exported on the world market.

Considering the huge number of goats in China, we can safely presume almost everyone in China who say he had eaten 羊肉 before, meant he had eaten 'goat meat' (not sheep meat).