You can get it from any Persian market with a freezer section. I don't know the South Bay very well. In the San Fernando Valley, the following places have it:
Araz International Market in Granada Hills
Valley Produce in Reseda
Q Market in Reseda
Woodland Hills Market in Woodland Hills
In West LA, I bet Rose Market or any of the Persian markets on Westwood Blvd. would have it.
In Glendale, I'm sure some of the Armenian-Persian markets would carry it.
I don't know of any Persian markets in Pasadena, but maybe others can chime in. :)
Sorry, I just looked at your link, and you want an Indian drink that I know nothing about. I thought you were talking about the Persian frozen dessert that goes with ice cream, i.e., faloodeh.
I bet that you could find the Indian drink in Artesia somewhere. Good luck.
India Sweets and Spices in LA has it:
They have locations in Northridge, Culver City, Tustin, Glendale, Canoga Park, Duarte, San Diego, Fresno, and Thousand Oaks (coming soon). See the link below for exact addresses.
As a side note, I have been to the Glendale location on Los Feliz Blvd. I thought the service was lacking, but the mango lassi I got was okay. I've never tried Indian style falooda. Apparently, it's about $4 at India Sweets and Spices.