I think you need to replace your binding statement with the field name (see highlighted code) or use ItemsControl to show all attributes (see Grid).
<esri:FeatureLayer ID="MyFeatureLayer" Url="http://faith/ArcGIS/rest/services/MontgomeryJoined/MapServer/0" OutFields="*" DisableClientCaching="True">
<esri:FeatureLayer.MapTip>
<!--<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition Width="Auto"/>
<ColumnDefinition Width="*"/>
</Grid.ColumnDefinitions>
<ItemsControl ItemsSource="{Binding Keys}" Grid.Column="0" />
<ItemsControl ItemsSource="{Binding Values}" Grid.Column="1" />
</Grid>-->
<TextBlock Text="{Binding [Montgomery.DBO.owners.DEED_DATE]}"/>
</esri:FeatureLayer.MapTip>
</esri:FeatureLayer>