No matter what I tried, I could not get the drill through to work in the chart - despite the fact that it was working perfectly in the tabular report. After some investigation I realised that this is caused by the time series functionality that is switched on in the horizontal axis and the drill functionality is not available for time series charts. Yellowfin will, by default, convert any date field on the axis to a time series field.
After the time series functionality was disabled on the horizontal axis, the drill through worked fine. If you would like to read more about time series charts, I would recommend this article.
On the Yellowfin WIKI pages there is this very handy table on drill functionality by chart type.