Hi Jimmy,
It is possible. In fact, it is not so difficult to achieve. Follow these instructions:
1) Go to http://tiledbasemaps.arcgis.com/arcgis/rest/
2) Paste required token. To get token, you need create developers.arcgis.com or arcgis online account (it is free).Log in to developers.arcgis.com. Next, Click Applications >Register New Application (give a name and description - whatever you want)> Register New Application > Generate Token
3) Select the basemap of your choice (i.e. World_Street_Map) and click Export tiles or paste URL http://tiledbasemaps.arcgis.com/arcgis/rest/services/World_Street_Map/MapServer/exportTiles
4) Fill in all required parameters. You will find some help about Export Tiles task here
For Export extent specify boundary of the tpk, you want to generate. xmin , xmax etc. are in decimal degrees, for example 10.233
For Export By specify LeveID. Below add the level numbers: 1(smallest scale) 19 (the largest scale). Above only 1 to 13 levels are requested.
Watch out the maximum tiles to export constraint. It is set to100 000 tiles. If you encounter such error, adjust the number of cache (tiles) levels or extent to export.
5) Click Export tiles (POST). Tile generation process has been started.
6) After a while, click Check Job Details Again- it checks the status of geoprocessing.
7) As soon as the process has been finished, you will get the results by clicking out_service_url
😎 Copy value field content URL to the new browser tab
9) Click Layers.tpk to download the data
You are ready to go!