Hi Adam,
... calibrate a set of data using Darks, Flats, and Biases that were created outside of PI using another software.
In general, that won't work. The main problem is that the FITS format does not define any standard way to describe the numeric range to which floating point data are referred. This has been discussed many times on this forum. Each application follows its own rules, which are in most cases undocumented. In the case of PixInsight, floating point images are always stored in the [0,1] range, where 0=black and 1=white. However, with the sole exception (AFAIK) of DeepSkyStacker, the rest of applications don't follow this rule. Without a common numeric range of reference, calibration masters lose their physical meaning and hence are unusable.
You can try with input hints to adapt the alien data to PixInsight. Depending on the other application, this may or may not work. Input hints are special control words that modify the way file format modules work in PixInsight. For example, try the following:
upper-range 65535
which should work if the other application stores floating point data using a 16-bit integer range.