Flex rendered my chart labels too about 4 pixels high. This is what the documentations says about this topic:
When positioning and sizing labels, the AxisRenderer takes a minimum amount of the chart’s available space. If labels take too much space, then the AxisRenderer scales them. However, the AxisRenderer does not scale the labels to too small of a point size.
After some trial and error, I found out that this is not true if you use the gutter properties. For my ColumnChart I used both gutterLeft and gutterRight to a fixed value. Once I didn’t set the gutterRight property, the labels were rendered to decent sizes.