The Illinois Policy Institute has examined IRS data, and thinks this is a problem. Texas and Florida appear to be prime destinations, see

The real problem appears, however,  to be attraction of new residents, since an aging population moving to warmer climates may have nothing to do with tax burdens, see
Past increases in income taxes have, somewhat unexpectedly, been associated with increases in high net worth tax filers in Illinois. It is lower income residents who are moving out for other opportunities, and not finding new jobs here. Restrictions on immigration probably have an effect on that cohort, as well. See generally
Where do you want to live? Here, or down in the very large bugs, floods, and heat wave zones? Our family’s choice to stay here so far is obvious– but then, we would be more likely to move North to be with a grandchild, so our motivations aren’t the same as many others. Church, friends, family, jobs, and weather can all play a role in migration. With any luck, we will get our act together as a state, and start attracting a few more new neighbors.

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