Whisk cornstarch or other thickener into creamer until dissolved. Set aside.
Wash mushrooms, cut off browned stems if necessary, and halve or quarter if large.
Heat butter in skillet or saucepan over medium heat until sizzling. Add mushrooms and shallots and saute until mushrooms begin to render their liquid, about 2 to 3 minutes.
Stir in port and simmer rapidly until reduced by about a third. Add the creamer mixture and whisk until thickened and beginning to boil, about 2 to 3 more minutes. Adjust seasonings. Set aside.
Wash the chicken breasts and pat them dry. Flatten to 1/2" thickness by pounding with the flat end of a meat mallet or other heavy kitchen item between two sheets of plastic wrap, waxed paper, or parchment paper.
Dredge breasts in almond flour and set aside. Heat a heavy skillet over medium heat and add fat.
Saute chicken breasts in fat 3 to 4 minutes until the bottom is browned slightly; turn with tongs and saute the other side. Test with instant-read thermometer and chicken should be done when temperature reads 165 degrees F.
Plate each breast and top with sauce. Serve immediately.