How to estimate size of cloud formation
Three methods spring to mind:

1) If you can really estimate both the width in degrees and distance to the cloud, you can draw a triangle and use trigonometry to calculate the width. 

2) The distance to the cloud you may estiamte from the cloud type. But both height and width in degrees are uncertain numbers. Instead you can estimate cloud sizes by looking at planes passing through them. If you time how long it takes a plane to pass through a cloud, you can multiply that with its cruising speed to get the width of the cloud. The cruising speed (typically 500km/h) can be found via say, the Flightradar24 app.

3) Using that app, you can also track the plane in real-time to map out not only the length of the cloud, but what land it is covering. No need to time the plane or know its speed.

By following a plane on the app until it goes under the horizon at your location, you get a feel for "how far away the horizon is", for clouds at that plane's altitude. high-altitude clouds and aurora at the horizon will be much farther away than low-altitude clouds.