If your flatware collection is sterling silver, you can find an appraiser by contacting your insurance agent who can recommend a reliable professional. Or you can look up the American Society of Appraisers and find on in your area.
If the flatware is silver plate, it will be of far less value, and it may not be economical to pay the high price of an appraiser. Check the bottom of each spoon to see if they are sterling or silver plate. A silver plate can be found in thrift shops. Attractive or interesting silver plate is often sold online in sites like Etsy. Even if it's silver plate if you sell them for one dollar a piece you can earn hundreds of dollars.
The demand for sterling is not what it once was, and certain patterns are more desirable. So the value depends on the manufacturer, age, condition, and pattern.