How to change the border color of a flat button style
<Style TargetType="Button" x:Key="FlatButtonStyle">
    <Setter Property="Background" Value="Transparent" />
    <Setter Property="BorderBrush" Value="Transparent" />
    <Setter Property="Margin" Value="2" />
    <Setter Property="FontSize" Value="30" />
    <Style.Triggers>
        <Trigger Property="IsFocused" Value="true">
            <Setter Property="BorderBrush" Value="#E01919"/>
        </Trigger>
    </Style.Triggers>
</Style>

<UserControl.Resources>
    <Style x:Key="Flat">
        <Setter Property="Control.BorderBrush" Value="{x:Null}" />
        <Style.Triggers>
            <Trigger Property="Control.IsMouseOver" Value="True">
                <Setter Property="Control.BorderBrush" Value="{x:Null}" />
            </Trigger>
        </Style.Triggers>
    </Style>
</UserControl.Resources>
<StackPanel>
    <Button Style="{StaticResource Flat}">Hello</Button>
</StackPanel>