You’re missing one slash in your path and try to pass it as an FName not as regular string, so it should look like this:
// note that '/' operator for strings will add them together but will also put '/' in between
FString ImagePath = FPaths::GameContentDir() / TEXT("default_pictures/test.jpg");
FName BrushName = FName(*ImagePath);
....
SNew(SImage)
.Image(new FSlateImageBrush(BrushName, FVector2D(128, 128)))
....
I’ve tested it on .png file but it should work with .jpg just fine.
Also, if you would like to have dynamic brush on SImage take a look into FSlateDynamicImageBrush class, there are some examples in UE source code.