Why should I roll the meat in flour for a ragout Most recipes for ragout call for rolling the meat in flour before adding, including one recipe whre you don't sear the meat but add it with the vegetables and everything else once the onions are done. What is the function of the flour, especially in the latter case?
Flour is a thickening agent, plain and simple. However adding it without cooking it first can lead to your dish having a raw flour taste, and you can get blobs of flour in it, so I would ignore the recipes which say coat with flour without cooking it first, or use cornstarch (cornflour) instead. 

Alternatively you can make a roux with flour in a separate pan and add it in later. This is simply mixing equal weights of flour and butter and cooking it in a frying pan until it has the color you want. A lighter roux will add a paler color and a milder flavor, a darker roux adds a deeper color and richer flavor.