Herb Flowers (Cinnamon Basil)

I'm new to herb gardening and have two questions. My cinnamon basil now has small flowers on the ends of the stems. Should the flowers be used in cooking or should they be clipped? Generally, when herbs are picked should they be washed before use?

This is true for all herbs – if you want plants to keep producing their leaves and flavourful oils, vs. going into seed production, you should pinch off the flowers and or seed pods. Pruning plants buy periodically pinching off leaves or snipping branches will also stimulate leaf production and branching (rosemary). When removing leaves to use, go around outside edges generally (chives, parsley, it depends on the herb and where the new growth is coming from). Look where the new leaves are growing and make sure not to touch the small leaves that are just starting. Basil for instance sprouts new leaves in the space between stem and branches (I call it the arm pits). Pinch off the branch but leave the new ones to mature. When plants are young and small, only take about a third of the leaves. Doing this will ensure larger, fuller plants. Some herbs such as coriander (cilantro) and dill will go to seed (bolt) very quickly so removing the flowers and seeds is important if you want lots of leaves. (Don't just let herbs grow until the end of the season and harvest the whole plant at once.) You might want to let coriander go to seed. This seed can be ground for cooking. It also self-seeds and new plants will start to grow below the parent plant, which is great if you are in a climate with a longer growing season.
Herb flowers make beautiful garnishes for plates, dessert, soups, etc. Pinch off flowers and a few of the nearby leaves. I rinse and store mine in the refrigerator, in a rectagular plastic container (then they are all ready to use) that I line with a few layers of slightly damp paper towel. Most will keep like this for several days.
Do rinse all herbs, but do it just before you will use them. This is to prevent overhandling and bruising of leaves (especially basil) to prevent release of the volatile oils and the browning of the leaves. For cleaning large amounts of herb leaves I use a salad spinner to rinse and dry them. Several rinsings may be necessary if the leave have sand or dirt on them. Rinse until you do not feel any grit in the bottom of the spinner bowl.
Herb flowers have the same flavour as the herb the come from, sometimes more intense (chive flowers). You can use the flowers whole as a garnish or break them up into small florets to toss into a salad or soup for instance, when they are more likely to be eaten. Herb flowers can also be used to make herb butters and are attractive in herb vinegars. At the end of the season I often make a bouquet of herbs that have flowered (purple basil, sage, garlic chives, rosemary).