Sure you can eat them. Harvest them when they look like beans that you would get from other bean plants. They're a little larger than bush beans.

I need to remember to plant some next year....

Scarlet runner beans are a vegetable not a flower. They are an attractive plant and often used as a flower. They look great on a trellis or arbor and the bonus is delicious beans. They are longer than bush beans and should be havested when they are firm and full. Wait too long and they won't be good.

Further to Oilpainter's advice, I would suggest harvesting them when they're less than 1/2" wide or they become very tough & fibrous. Then you can eat them like any green bean. If you leave some to go to seed they make very cool looking pink and black bean seeds up to an inch long.

If they dry then you need to use them for baked beans.

Runner beans come in several forms other than scarlet.
There are salmon, white and bicolour forms.
Also there is a dwarf form.

Caroline