Utilizing the Javascript based leaflet mapping tool can be done easily with the leaflet() package in R. Below is an example that projects 1 km netCDF data and a JSON polygon (converted from a Google Earth KML file) on top of the standard interactive leaflet street map.
library(sp)
library(ncdf4)
library(leaflet)
library(raster)
library(rjson)
netCDF_file <- "/Users/charlesbecker/Desktop/Globus Data/test-06-11-05.nc"
jsonFile <- "/Users/charlesbecker/Downloads/SR_AVA_simplified_pointRemove50m.json"
# convert JSON file to R list object (this is just an additional shape layer)
json <- fromJSON(file = jsonFile)
# Pull the lattitude and longitude from the NetCDF file
lattitude <- raster(netCDF_file, varname="XLAT")
longitude <- raster(netCDF_file, varname="XLONG")
# Convert to points and match the lat and lons
pointLat <- rasterToPoints(lattitude)
pointLon <- rasterToPoints(longitude)
longLat <- cbind(pointLon[,3], pointLat[,3])
# Add Coordinate Reference Sysytem to longLat
longLat <- SpatialPoints(longLat, proj4string = CRS("+proj=longlat +datum=WGS84"))
# define CRS from netCDF file
myCRS <- CRS("+proj=lcc +lat_1=44.3f +lat_2=44.3f +lat_0=44.10741f +lon_0=-115.6207f +units=m +datum=WGS84 +no_defs")
plonlat <- spTransform(longLat, CRSobj = myCRS)
# Load raster and set projection and lat/lon extent
pr <- raster(netCDF_file, varname="T2")
projection(pr) <- myCRS
extent(pr) <- extent(plonlat)
# Project to the leaflet lat/long grid and visualize
r <- projectRasterForLeaflet(pr, method = "bilinear")
plot(r)

# set color palette
color_pal <- colorNumeric(c("#0C2C84", "#41B6C4", "#FFFFCC"), values(r),
na.color = "transparent")
# underlay basic leaflet map, overlayed with JSON boundary and raster grid
leaflet() %>% addTiles() %>%
addGeoJSON(json, weight = .5, color = "black", fill = FALSE, opacity = 1) %>%
addRasterImage(r, colors = color_pal, opacity = .7) %>%
addLegend(pal = color_pal, values = values(r),
title = "2M Temp")