Bill, assuming that you're registered (on the same email address) you don't actually need to download the route - you can simply access it from the app.

You don't say if you are using Android or IOS but in Android I:

Open the app

Tap the "Routes" icon (bottom of the screen)

Either choose the route from "My saved journeys" (or select the folder): It follows a similar layout to the website

Off I go.

I can't see it being a very different process on IOS.

If it's not working like that, check that the journey is not labelled as "private". I think that was an issue in the early days.

If, as your title suggests, you are looking to store a route on your phone to be able to access it offline there are a couple of extra steps:

Check that the general map area has been downloaded ("Settings", "Offline map")

Select the route (as described above) but this time "long press" - this will give the option of "Delete Route" or "Download to Phone". You can guess which one to choose :-)

You'll now see a phone symbol beside the route name. 

Click on this anytime to open the route.

On iPhone it’s the same, but when you’re in the route list, instead of long-pressing, swipe the route name to the right. You’ll see a blue “download” button appear – tap that. The route will be downloaded and the phone icon will appear.