You can get the markdown italic tags interpreted properly by adding format="markdown" as an argument to kable.
knitr::kable(
df, format="markdown",
booktabs = TRUE,
caption = 'Testing italics using kable'
)
Another option would be to use latex markup instead. That also requires adding the escape=FALSE argument to kable.
df <- data.frame(Standard = "This is standard",
Italics = "\\emph{This piece} should be in italics")
knitr::kable(
df, booktabs = TRUE, escape=FALSE,
caption = 'Testing italics using kable'
)