Your technique will depend on what XAML object your SVG to XAML converter produces. Does it produce a Drawing? An Image? A Grid? A Canvas? A Path? A Geometry? In each case your technique will be different.
In the examples below I will assume you are using your icon on a button, which is the most common scenario, but note that the same techniques will work for any ContentControl.
Using a Drawing as an icon
To use a Drawing, paint an approriately-sized rectangle with a DrawingBrush:
<Button>
<Rectangle Width="100" Height="100">
<Rectangle.Fill>
<DrawingBrush>
<DrawingBrush.Drawing>
<Drawing ... /> <!-- Converted from SVG -->
</DrawingBrush.Drawing>
</DrawingBrush>
</Rectangle.Fill>
</Rectangle>
</Button>
Using an Image as an icon
An image can be used directly:
<Button>
<Image ... /> <!-- Converted from SVG -->
</Button>
Using a Grid as an icon
A grid can be used directly:
<Button>
<Grid ... /> <!-- Converted from SVG -->
</Button>
Or you can include it in a Viewbox if you need to control the size:
<Button>
<Viewbox ...>
<Grid ... /> <!-- Converted from SVG -->
</Viewbox>
</Button>
Using a Canvas as an icon
This is like using an image or grid, but since a canvas has no fixed size you need to specify the height and width (unless these are already set by the SVG converter):
<Button>
<Canvas Height="100" Width="100"> <!-- Converted from SVG, with additions -->
</Canvas>
</Button>
Using a Path as an icon
You can use a Path, but you must set the stroke or fill explicitly:
<Button>
<Path Stroke="Red" Data="..." /> <!-- Converted from SVG, with additions -->
</Button>
or
<Button>
<Path Fill="Blue" Data="..." /> <!-- Converted from SVG, with additions -->
</Button>
Using a Geometry as an icon
You can use a Path to draw your geometry. If it should be stroked, set the Stroke:
<Button>
<Path Stroke="Red" Width="100" Height="100">
<Path.Data>
<Geometry ... /> <!-- Converted from SVG -->
</Path.Data>
</Path>
</Button>
or if it should be filled, set the Fill:
<Button>
<Path Fill="Blue" Width="100" Height="100">
<Path.Data>
<Geometry ... /> <!-- Converted from SVG -->
</Path.Data>
</Path>
</Button>
How to data bind
If you're doing the SVG -> XAML conversion in code and want the resulting XAML to appear using data binding, use one of the following:
Binding a Drawing:
<Button>
<Rectangle Width="100" Height="100">
<Rectangle.Fill>
<DrawingBrush Drawing="{Binding Drawing, Source={StaticResource ...}}" />
</Rectangle.Fill>
</Rectangle>
</Button>
Binding an Image:
<Button Content="{Binding Image}" />
Binding a Grid:
<Button Content="{Binding Grid}" />
Binding a Grid in a Viewbox:
<Button>
<Viewbox ...>
<ContentPresenter Content="{Binding Grid}" />
</Viewbox>
</Button>
Binding a Canvas:
<Button>
<ContentPresenter Height="100" Width="100" Content="{Binding Canvas}" />
</Button>
Binding a Path:
<Button Content="{Binding Path}" /> <!-- Fill or stroke must be set in code unless set by the SVG converter -->
Binding a Geometry:
<Button>
<Path Width="100" Height="100" Data="{Binding Geometry}" />
</Button>