Wash all greens, and shake off excess (but not all) water. Heat a large saute pan over high heat, and add kale, collards, 1 teaspoon salt, and wine. Cover, and cook until greens wilt, about 2 minutes, turning occasionally. Reduce heat to medium, and cook, turning greens occasionally, until almost tender, about 15 minutes. Remove cover. Add chard leaves, and cook, turning with tongs, until wilted, about 3 minutes. Transfer greens to a bowl.
Add 4 tablespoons butter to pan, and melt over high heat. Add shallots, garlic, and chard stems, and saute until softened, about 3 minutes. Stir in chestnuts, and saute 1 minute. Return greens to pan, stirring to incorporate, and remove from heat.
Melt remaining 2 tablespoons butter in a saucepan over medium-high heat. Add flour, and whisk to incorporate. Slowly whisk in milk and cream, and bring to a simmer. Simmer, whisking constantly, until sauce thickens slightly and begins to coat the back of a spoon, about 2 minutes. Add nutmeg and red-pepper flakes. Season with salt.
Stir sauce into greens, and cook over medium heat until warmed through. If not serving immediately, let cool completely, then refrigerate. Reheat over low heat before serving.