The most common and most likely answer to this crossword clue is the 6 letter word FLUTED
I've seen this crossword clue in The Daily Telegraph
F
L
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D
More clues leading to the result FLUTED
Buddy explains!

The straight part
We know that "fancy grooves" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fancy grooves = fluted.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FLUTED mean?
FLUTED verb- To play on a flute.
- To make a flutelike sound.
- To utter with a flutelike sound.
- To form flutes or channels in (as in a column, a ruffle, etc.); to cut a semicylindrical vertical groove in (as in a pillar, etc.).
- Having flutes or grooves, either for decoration or to trim weight.
- Drunk; intoxicated.