ray1761 - my 2 cents worth is that you would have to go to a more complicated linkage arrangement than a rod & lever arm in order to match the non-linear flow curve. Maybe I'm being Master Of The Obvious and you already know that, but it is more of an operation than what you mentioned of:
"By connecting the linkage in the correct location on the arms of the valve and the actuator, I should be able to get a linear flow output through the valve that corresponds with the actuator position"
You've got to have a mechanism which will match (or approximate closely enough) the exponential (or quadratic or partial sine wave or whatever it is) flow curve. Then, like terje61 said, if densities and pressures change, it will shift the curve. Maybe that is splitting hairs too much and you aren't interested in that tight of control, just in following the general shape of the curve and being "in the neighborhood".
The first step is a good ol' exercise in Analytical Geometry, evaluating the flow curve to get a mathematical approximation. That is not too daunting a task for someone, unlike me, who remembers that stuff. Or some "CFD" program (Computational Fluid Dynamics) should be able to handle it. Then the next step is an exercise in Kinematics, designing a linkage arrangement to approximate your mathematic relationship. I don't remember if you can get there using a combination of circular arcs (lever arms). It is likely going to be a slotted plate/follower type arrangement, but the slot will need to be custom machined to generate the proper motion.
(Now just having said that, and having had another swig of Diet Pepsi this morning, it strikes me that surely someone already makes such a device. It would have to be adjusted/tuned to each installation, but we're not talking space travel here, just getting closer to the curve than the linear actuator.)