A few questions

[Swami Vishvarupananda]

> Advaita is based on the Tantras whereas Kashmir Shaivism is based
> on the Shaivagamas but other than that how compatible or incompatible are
> they?

Just a little correction in the beginning. You can't say, Advaita and
Kashmir Shaivism. Kashmir Shaivism is as much Advaita as Advaita Vedanta
and so are several other schools of thought.
Advaita Vedanta is based on the Tantras? This is very interesting. I was
always the opinion the Tantras are mostly criticized by Vedantins.
Kashmir Shaivism is, as you rightly say based on the Shaivagamas, but also
on Tantras, like Malinivijayottara Tantra, which belongs to its scriptures.

For an introduction to Kashmir Shaivism you may read the well presented
Paper: THE UNIQUE POSITION OF THE SPANDA SCHOOL AMONG THE OTHERS OF THE
TRIKA SYSTEM OF KAZMIR, by E. Garzilli in the International Journal of
Tantric Studies at
http://www1.shore.net/~india/ijts/issue1/index.htm#art1

Greetings and Om,
Swami Vishvarupananda