When do the flowers of the Family Primrose (Primulaceae), especially
flowers of the genus Androsace, bloom in Ladakh, India? I'm trying to
figure out when is the best time that I should vacation in India this
summer so that I can see these flowers.

Primroses of the sort you’re looking for, Primulaceae, Andrsace, bloom
in July and August in the high altitudes of the Himalayas. The
following chart is from:

Plants of Bhutan
http://www.fao.org/docrep/X5335e/x5335e07.htm

Androsace primuloides Duby 	Primulaceae 	3,000-4,300 m. 	July-August 

This site essentially agrees:

Rock Garden Plants – Family: Primulaceae, Genus: Androsace  robusta
Hand.-Mazz.
http://web.kadel.cz/flora/c/kvCard.asp?Id=9140

These flowers bloom in the summer, and grow at altitudes of 3100-5000
meters (10170-16404 feet).

While Buthan and Ladakh are separated by many kilometers, the climates
and vegetation of the Himalayas, which span these area, are dependant
primarily on altitude; the average elevation of Ladakh is 2700-4200
meters.

Himalayas – Flora and Fauna
http://library.thinkquest.org/10131/ff.html

From this information, it appears that the best time to see the
primroses of the area is in July and August, and either of those
months should find many blooming flowers.

Other sites of interest:

Best Time to Travel the World
http://travel.ninemsn.com.au/getaway/askgetaway/2001/32/askgetaway7.asp

Maps of India
http://www.mapsofindia.com/

Flora and Fauna of Kangchendzonga National Park, Sikkum
http://library.thinkquest.org/10131/ff_kangchend.html?tqskip1=1&tqtime=0427

Explore “Little Tibet” with Discover Asia
http://www.asiantraveladventures.com/india/ladakh.htm

Excellent and concise and provided me with a well-reasoned answer.
This worked just as I has hoped it would.