You may be able to just grab the shapefiles from NGA: (U) Military Grid Reference System (MGRS) 100km Polygon Shapefile (.shp) Downloads (UNCLASSIFIED) and use those directly in Tableau.
I don't think shapefiles would work.
I would need 3 different shapefiles, one for each level, correct?
The 1KM shapefiles seem to only be for select bigger cities, there doesn't seem to be a shapefile that has 1KM for the entire US.
You can put together a 1km dataset for the whole US by downloading the individual bits from here: http://earth-info.nga.mil/GandG/coordsys/grids/mgrs_1km_polygon_dloads.html
But…based on the size of one of the download files you might not want to try making the 1km dataset for the whole US. It would be ~26 different zones, and the one that I downloaded was ~230mb unzipped as a shapefile. Converting to a .Hyper extract will take it down to about 50mb...but, again, that just covers one small part of the US.
There is also a geodatabase that looks like it has a larger set of 1km polygons in a single file, but that is a 24GB download!
If you wanted to match up to three different levels of detail with the grids, yes, you would need three different datasets. But, you should be able to union them all together into one dataset if needed.