Your sample code has a double equal sign in the App.xaml merged resource dictionary source for Palette.Blue.xaml. I'm assuming this is a typo for your example posted here, and not your real problem though.
It can be tricky to figure out how to link all the resources directly in XAML. The easiest way to do it is from the Resources panel in Blend. I created a Silverlight app with resource files named like your example, then opened the project in Blend and very quickly linked them together.
App.xaml
<Application xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" x:Class="SilverlightApplication1.App">
<Application.Resources>
<ResourceDictionary>
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary Source="Theme.xaml" />
<!--
<ResourceDictionary Source="Palette.Blue.xaml"/>
<ResourceDictionary Source="Template.xaml"/>
-->
</ResourceDictionary.MergedDictionaries>
</ResourceDictionary>
</Application.Resources>
</Application>
Theme.xaml
<ResourceDictionary xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<ResourceDictionary.MergedDictionaries>
<ResourceDictionary Source="Palette.Blue.xaml"/>
<ResourceDictionary Source="Template.xaml"/>
</ResourceDictionary.MergedDictionaries>
</ResourceDictionary>
Template.xaml
<ResourceDictionary xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<Style TargetType="TextBox">
<Setter Property="Margin" Value="10" />
<Setter Property="Width" Value="250" />
</Style>
<Style x:Key="ReadOnlyTextBoxStyle" TargetType="TextBox">
<Setter Property="IsReadOnly" Value="True" />
<Setter Property="Foreground" Value="Black" />
<Setter Property="IsTabStop" Value="False" />
<Setter Property="Margin" Value="10" />
<Setter Property="Width" Value="250" />
</Style>
</ResourceDictionary>
Palette.Blue.xaml
<ResourceDictionary xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<SolidColorBrush x:Key="BlueSolidColorBrush" Color="SkyBlue" />
</ResourceDictionary>
MainPage.xaml
<UserControl x:Class="SilverlightApplication1.MainPage" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml">
<StackPanel x:Name="LayoutRoot" Background="Honeydew">
<TextBox Text="Read Only Textbox"
Style="{StaticResource ReadOnlyTextBoxStyle}" />
<TextBox Text="Blue Textbox"
Background="{StaticResource BlueSolidColorBrush}" />
<TextBox Text="Read Only, Blue Textbox"
Style="{StaticResource ReadOnlyTextBoxStyle}"
Background="{StaticResource BlueSolidColorBrush}" />
</StackPanel>
</UserControl>
Of course, if you're linking resources from different assemblies it will look different. Actually, in that case, I'd suggest looking into merging your dictionaries in the code behind.