Ask Mr. Smarty Plants

There are 50 species of the genus Castilleja native to North America and 17 native to Oregon, so we searched those for one that seemed most likely to be growing in your area. Castilleja applegatei (wavyleaf Indian paintbrush) grows in Deschutes County, OR according to the USDA Plant Profile. It also looks very similar to the Indian Paintbrush that we are familiar with in Texas and we will use it for our example. 

"Propagation

Propagation Material: Seeds
Description: Seed in open, sunny sites for best results. Indian paintbrush seed may require a cold wet period in the winter to germinate. Plant the seed in the fall and rake it into loose topsoil to ensure good seed/soil contact. Seeds are exceptionally small (4 million seeds per pound), commercially available, depending on the previous year’s seed crop and can be expensive. The recommended seeding rate in 1/4 pound per acre.
Seed Collection: Seeds are formed in capsules at the base of each flower. Seed capsules may be carefully collected by hand April – May when the capsules are dry and brown.
Commercially Avail: yes
Maintenance: After flowering ceases, allow seeds to completely mature before mowing for reseeding or collecting to plant in a new area. Since C. indivisa is an annual, it is essential that this species be allowed to reseed for an abundant display for the following year."

From the website Dave's Garden, we found these instructions on the specific Castilleja applegatei (wavyleaf Indian paintbrush) from personal experience:

"I've since collected seeds from that original plant and have now established this paintbrush in over 20 locations in my garden. I simply collected the seeds as soon as the stems appeared completely dry and scattered them immediately upon the surface of bare un-amended soil somewhere near a known host plant--such as Wright's Buckwheat--'Eriogonum wrightii'. My original Applegate's Paintbrush is also still flourishing and expanding it's terrritory in my dry rocky soil, but the Scarlet Penstemon from which it sprang seems to have succumbed to the parasitical nature of the castilleja." 

The timing of collecting the seeds of Castilleja indivisa (entireleaf Indian paintbrush) may be a little off, since we are in USDA Hardiness Zone 8a and you appear to be in Zone 6a. In you were in Texas, it would already be past the time for collecting seeds, but in Oregon, this may be the time. As you note in the references above, the seeds are very tiny. The plant is an annual, so reseeding from the original is really the only way to keep the flowers in your garden, short of buying seeds every year. You also need to remember that this plant is hemi-parasitic, requiring that there be nitrogen fixing plants in the near vicinity for use by the paintbrush roots. 

From our Native Plant Image Gallery:

Castilleja applegatei

Castilleja applegatei

Castilleja indivisa

Castilleja indivisa