Are you looking at a retrograde greenschist assemblage of rocks, originally a much higher grade assemblage?
Is the greenschist facies rock already at a high enough pressure to make kyanite?
Look hard at your thin sections to determine whether the rocks show evidence of several stages of metamorphism and or retrogression with out of context replacements etc.
In the presence of excess SIO2 and Al2O3 in greenschist facies along with high pressure conditions, Kyanite is possible in associtation with Quartz and others.
(ref: Physiographic, Stratigraphic and Structural Development of the Quadrilatero Ferrifero Minas Gerais, Brazil, US Geological Survey Professional Paper - Page C33.)
Absolutely right Karthikeyan, so it is very important to know what the greenschist actually is. Is it prograde or retrograde, are there relicts that show amphibolite or higher grade metamorphism, what is the geological context, is it in a suture zone? Very important to have the mineralogy in context with structure and geology as well as details of the PT history.
The country rocks that I am referring to are very low grade greens hosts, that have preserved sedimentary structures like bedding. It hasn't been metamorphosed to higher grade of kyanite facies.
Another important information is that, the country rocks in which these small kyanite-quartz verins are found are also very rich in muscovite so much so that it occurs in veins.
So it is possible that excess silica and al2o3 plus some high pressure along cracks (I don't know how), must have led to the formation of these veins.
The country rocks are exposed along the coast of western continental margin of India.