Q:

How do I Read Bansuri Notation

How do I read Bansuri Notation 
Mumbai theme - A R Rahman
I know SA RE GA MA PA DHA NI SA, and the concept of low and high octaves. 
How do I correlate the letters.  And where are the letter different colors, i.e. Blue, Pink, or Red? 

A:

The notes in blue are to be played in the madhya sthāyi (middle octave), the notes in red in the mandara sthāyi (lower octave) and the notes in pink in the tāra sthāyi (upper octave). 
I might add that it is not the standard practice to colour code the notation to indicate the octave.  In Carnatic (south Indian classical) music, a dot above the note signifies the upper octave and a dot below the note signifies the lower octave; possibly the same notation is used in Hindustani (north Indian classical) music as well, but I am not completely certain. 
I observe that the author of the notation has (in addition to the colour coding) used an apostrophe to indicate the octave of the note.  So, 'N is the nishādam in the lower octave and R' is the rishabham in the higher octave. 
Since you ask how to correlate the letters, I presume you mean how to correlate them with the natural rhythm of the song?  The given notation is not very helpful in this regard.  It ought to have been partitioned into sets of 4, at the very least. 
You'll have to intuit this aspect, or obtain a better source of notation from elsewhere. 

I'd also like to mention that the author of the notation has shifted the shadjam by a few notes.  As the song starts you can hear the drone (shruti) in the background, which indicates the shadjam.  When the flute begins, it is then clearly at the panchamam, and not the gāndhāram as in the given notation.  So, the author of the notation has shifted the shadjam by a few notes down.  This changes some things, for instance the ragam that the song is based on, etc.  But, you ought to be able to play the song roughly in tune even with the given notation. 

Edit (in response to the comments below):
The song naturally follows a rhythm that can be counted in cycles of 4 (or 8) units.  So, I would notate the song with such indicators.  For example, the first line could be better written as:

g,,g,,g,    g,,g,,r,    m,g,r,r,    s,'n,s,'n,

This is better than bunching the notes together without sufficient indicators, as in the given notation.