1. Wash greens and shake off excess water.
2. Heat a large skillet over high heat, add kale, collards, 1 teaspoon salt, and the wine; cover and cook until the greens wilt, about 2 minutes.
3. Reduce heat to medium, cook the greens until they are almost tender, turning occasionally, about 15 minutes; remove lid and add the chard leaves, cooking and turning about 3 minutes, then remove to a bowl.
4. Add 4 tablespoons of butter to the skillet and melt over high heat; add the shallots, garlic, and chard stems and saute until softened, about 3 minutes.
5. Stir in the chestnuts and saute 1 minute; return greens to skillet and toss to incorporate, then remove from heat.
6. Melt remaining 2 tablespoons of butter in a saucepan over medium high heat; whisk in flour, then slowly whisk in milk and cream.
7. Simmer, whisking constantly, until sauce thickens and begins to coat the back of a metal spoon, about 2 minutes; whisk in nutmeg and pepper flakes, season with salt.
8. Stir the sauce into the greens and cook over medium heat until heated through.
9. If not serving immediately, cool completely and refrigerate; reheat over low heat.