Hi,
Whether you will see Cantera use multiple cores for a single solve depends on a few things. First, as far as I know, only the ReactorNet-compatible classes are able to use multiple cores, because they are linked to SUNDIALS (CVODES) which can be linked to parallel BLAS/LAPACK implementations that use multiple threads. The solvers for 1-D flames are not linked to libraries that use multiple threads, if I recall correctly.
Second, it depends on how you install Cantera. I don't recall exactly which platforms support which libraries. I feel fairly certain that with Anaconda on Linux and macOS, SUNDIALS is linked to either MKL or OpenBLAS, and Accelerate (respectively) all of which I believe use multiple threads to solve the linear algebra problems. If you install Cantera on Windows or from PyPI, I'm not sure if those capabilities are enabled.
Lastly, if you're building from source on macOS, we do link to the Accelerate library automatically, as I mentioned. On other platforms, you usually need to specify the correct BLAS/LAPACK yourself via configuration options.
Hope that helps!
Best,
Bryan