One simple workaround is to set the FlatAppearance.BorderColor of the Button to its Parent.BackColor
:
this.button1.FlatAppearance.BorderColor = this.button1.Parent.BackColor;
You could set this Property subscribing to the ParentChanged event (or overriding OnParentChanged, if it's a Custom Control) if the Control can be assigned to another parent at some point.
You can also perform the same operation in batch, using the HandleCreated event and have all the Buttons (with FlatStyle = FlatStyle.Flat
) subscribe to the event in the Form's constructor:
public Form1()
{
InitializeComponent();
foreach (Button button in this.Controls.OfType<Button>().Where(btn => btn.FlatStyle == FlatStyle.Flat))
{
button.HandleCreated += (s, e) => {
button.FlatAppearance.BorderColor = button.Parent.BackColor;
};
}
}