Jim,
You can find this answer this answer in the EC table of the INA196:
The content under output voltage shows that for a V+ of 3.3V, the maximum worst case swing of the output is from 50mV - 3.1V. You should provide some small amount of headroom as well to avoid saturation.
It should also be noted that the swing to Vs and swing to ground are normally obtained with some amount of overdrive on the inputs, and therefore the range of swing includes both linear output region and nonlinear region. To ensure linear operation, you normally need to look to other device specifications. Here, I would look to the gain error specification on the INA196 datasheet, which shows that linear operation is guaranteed from a Vsense of 20mV to 100mV. We have a video here that serves as a great primer for getting started in this area.
If this linear range is too shallow, I would recommend having a look at the INA281, which is a newer version of this device.
