I do not know of a built-in way to do this in Visual Studio's Solution Explorer, which is where I presume you would like the option.
I also searched for a VS extension that adds this option to Solution Explorer and did not find one either. Even VSCommands' Solution Explorer enhancements does not seem to offer this option.
Now what you might consider is using Visual Studio's Object Browser (View > Object Browser or Ctrl+W, J) with its View Namespaces option enabled (its default being View Containers):
Scoped to My Solution, this seems to provide the flattened-namespaces view of a solution that you want.
UPDATE:
Following comments below, note that double-clicking types and members in Object Browser will open them to view & edit their code - similar to double-clicking files in Solution Explorer.
To help with switching between Solution Explorer and Object Browser, consider a couple possibilities.
1) Pin the Object Browser tab (and consider displaying pinned tabs in their own row via Visual Studio's Tools > Options > Environment > Tabs and Windows > "Show pinned tabs in a separate row" (under the Pinned Tabs section of Tabs and Windows options)):
2) Dock Object Browser with Solution Explorer, below it etcetera - especially if you have a lot of screen real estate: