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Most fluids are not very compressible at all. I doubt there are any fluids, flammable or not, that are much more compressible than water. Maybe 50% more compressible (at best a factor of 2), but I very much doubt there are fluids that are 3-4 times as compressible as water. Gases on the other hand are very compressible. Solids and liquid not so much.
In general, organic solvents tend to be more compressible than water. See the Web Links for some values and other information. It looks like ethanol is about twice as compressible as water, although it is flammable, and so is carbon disulfide, but that is also flammable.
From the original questioner: According to the CRC Handbook, ethyl ether has a bulk modulus of around 15e-6 per dbar re: water at 4.4 e-6 per dbar; so that is about 4 times but this is both the ether of anesthesia fame as well as volitile and flammible i'm after some 'magic fluid' with even better compressibility (5 to 10 times) and not so dangerous, i guess it doesn't exist! thanks! Reply: You do realize of course that there are many gases that are both compressible and not flammable. Of course much much harder to contain and deal with, but would easily satisfy the other two requirements... just a thought.

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Q: Is there a fluid with very high compressibility at least 3 or 4 times of water and not flammable?
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