Summary: I have no citation but my understanding is that measuring insulin levels needs to be done from a blood draw, so a Freestyle Libre-type device wouldn't work.
The Freestyle Libre and regular continuous glucose monitors measure glucose in the interstitial fluid under the skin - not blood. This is why the numbers can be wildly different to a blood glucose test done via finger-prick.
From what I've seen while researching very low carb diets, insulin levels are incredibly important and influence a lot of body chemistry. For example, someone without type 1 diabetes can have a normal blood glucose but only because they're producing an enormous amount of insulin. A large amount of insulin in the blood will cause fat to be stored, so the patient puts on weight.