Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Blountville to Reykjavik as you normally would.
For a flight from Blountville to Reykjavik, you will be flying from Tri Cities TN/VA. Blountville Tri Cities TN/VA (TRI) is just 5.7 mi from the center of the city. Tri Cities TN/VA is the only Blountville airport and it handles 0 outbound flights to Reykjavik per day. 0 airlines have flights to Reykjavik from Blountville Tri Cities TN/VA on a regular basis.
These are just IATA (International Air Transport Association) codes. They are used in aviation to identify and differentiate airports. That’s why a Blountville Tri Cities TN/VA Airport to Reykjavik Keflavik Intl Airport flight would often be abbreviated as a TRI to KEF flight. Reykjavik Domestic Airport (RKV) are other airports near this flight route and their unique identifiers/IATA codes.