My data is in USA Contiguous Albers Equal Area Conic projection. How can I convert the USA Contiguous Albers Equal Area Conic projection to miles?
You have to create a custom CRS with miles as units, like
+proj=lcc +lat_1=33 +lat_2=45 +lat_0=39 +lon_0=-96 +x_0=0 +y_0=0 +datum=NAD83 +units=mi +no_defs
Then save your data to that CRS and turn on-the-fly-reprojection OFF.
Unfortunately, the distance tools still writes
km as unit, but the USA is about 2886 miles wide, while it is 4649 km in the original lcc projection. This will be changeable in the upcoming new QGIS 2.8.
You need a recent version of QGIS, because older versions did not treat units other than meters and feet correctly.