Welcome to FT, peachessnc!

There's no direct flight from Nashville (BNA) to Frankfurt (FRA) so the flight you refer to (KL6142) is from Detroit (DTW) to FRA and as you say is operated by Delta. If you do a Google search for KL6142 the first hit will take you to http://www.flightstats.com/ where you will see:

(KL) KLM 6142
(DTW) Detroit, MI, US to (FRA) Frankfurt, DE
Operated by (DL) Delta Air Lines 142

So, yes KL6142 and DL142 are the same flight. I tried to check Delta's website but the response was so slow I had to give up.