The most common and most likely answer to this crossword clue is the 8 letter word SMOOTHER
I've seen this crossword clue in Financial Times
S
M
O
O
T
H
E
R
More clues leading to the result SMOOTHER
Buddy explains!

The straight part
We know that "flatter" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case flatter = smoother.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 SMOOTHER mean?
SMOOTHER adjective- Having a texture that lacks friction. Not rough.
- Without difficulty, problems, or unexpected consequences or incidents.
- Bland; glib.
- Flowing or uttered without check, obstruction, or hesitation; not harsh; fluent.
- (of a person) Suave; sophisticated.
- (of an action) Natural; unconstrained.
- (of a motion) Unbroken.
- (chiefly of water) Placid, calm.
- (of an edge) Lacking projections or indentations; not serrated.
- (of food or drink) Not grainy; having an even texture.
- (of a beverage) Having a pleasantly rounded flavor; neither rough nor astringent.
- (of a function) Having derivatives of all finite orders at all points within the function’s domain.
- (of a number) That factors completely into small prime numbers.
- (of a vowel) Lacking marked aspiration.
- (of muscles) Involuntary and non-striated.
- One who, or that which, smooths.
- In glass-cutting, an abrading-wheel for polishing the aces of the grooves cut by another wheel.
- A flatterer.