Wing root flares are not what many might think when it comes to flight performance gains.
In straight and level AoA trajectory there are no substantial gains between the same aircraft using or not using wing root flares. This should not be confused by the seperate criteria and affects of wing root to fuselage corner fillet. Although the flare does incorporate the corner fillet aspect they both provide alternate results. For the speeds of most ultralights corner fillets of 50mm radius provide a better reduction of interference drag than those of 10mm. For wing root flares 100mm to 150mm radius corner fillets at the flare provide much better results than 50mm fillets; there is no advantage going larger than this other than to cause discussion.
The two images above present this aspect of straight and level AoA flight (3.25deg incidence included). Both models return nominally equal Drag and Lift results within this flight mode regardless of air speed.
Where the wing root flare excels is within the intermediate AoA flight modes where the wing is transitioning through 4deg to 6deg AoA. Within this narrow band the flare reduces vortex turbulence generated by the contrast of upper and lower transient flow rejoining by channeling the free stream toward a more gradual reunification. This reduction in Drag on the aerodynamic example pictured, at 100kt and 6deg AoA, the flared wing provides about 65kg more Lift and 20% less Drag compared to the non flared model. This would occur during a situation such as a rate one turn, or, raised nose attitude cruise due to heavier AUW, or, glide approach. This aspect described above is presented in the two images below, the blue areas represent turbulent slower velocity air, the red represents higher velocity air, green represents free stream velocity of 100kt. Outside of this narrow performance band the wing root flare provides no advantage or hinderance.
So to conclude wing root flares are most effective during bank turns. They allow for tighter turns to be achieved over their non flared counterpart, and a more efficient cruise at higher AUW.
"No lawnmowers were harmed during these scientific experiments."