You will need to set the FlowDirection to a TextBox, not a DataGridCell. If you are using a DataGridTextColumn, then
<DataGridTextColumn ...>
<DataGridTextColumn.ElementStyle>
<Style TargetType="TextBlock">
<Setter Property="FlowDirection" Value="LeftToRight" />
</Style>
</DataGridTextColumn.ElementStyle>
<DataGridTextColumn.EditingElementStyle>
<Style TargetType="TextBox">
<Setter Property="FlowDirection" Value="LeftToRight" />
</Style>
</DataGridTextColumn.EditingElementStyle>
</DataGridTextColumn>
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