To anyone having this same issue, the answer is to set a background(it can be transparent) to the datagrid. That makes the flyout clickable and showable all over. Also, instead of using RowSTyle:
<Style TargetType="dataGridControl:DataGridRow">
<Setter Property="dataGridControl:DataGridRow.ContextFlyout">
Use:
<Style TargetType="dataGridControl:DataGrid">
<Setter Property="dataGridControl:DataGrid.ContextFlyout">
<Setter.Value>