Copy your folder with your tiles (VNM_msk_alt) inside a www folder under your working directory.
But when I try to visualize it with this code
leaflet() %>% addProviderTiles("CartoDB.Positron", group = "CartoDB.Positron") %>% addTiles(urlTemplate = "VNM_msk_alt/{z}/{x}/{y}.png", group = "DEM (SRTM) Vietnam")
After two or three zoom levels, i get to see something that looks like Vietnam, but sits west of Australia. Something is wrong with the projection.
Hope this helps.