with this speed it will take you about 12 hours to download the complete Iraq Mbtiles dataset (1500MB)...
for a quick solution: ArcBruTile uses local caching for tiles you've already retrieved. By default, after 1 day new tiles are retrieved. You can change this setting with the 'tileTimeout' parameter in the config file (see documentation)
if you want to use MBTiles locally in ArcMap with ArcBruTile this is not possible now but I'll put it on the work items list.