Why does an R2 of close to zero imply that a regression has no contiditional heteroskedasticity?

An R-square from which regression are you talking about?

The original regression R-square tells you *nothing* about heteroscedasticity.

If the R-square from a regression of the squared residuals (errors) on the independent variables has a value close to zero, then the x-variables have little explanatory power of the squared residuals. In a formal test of this model, you might find that the x-variables cannot predict the squared residuals. In other words, no conditional heteroscedasticity.