Quick answer
Flattery is trapping equipment. The verse leaves it deliberately unclear whose feet the net is under.
Read both lines
The Hebrew is ambiguous about the pronoun and the ambiguity is probably intentional. The net is spread עַל־פְּעָמָיו, for his steps, and the referent can be the neighbor being flattered or the flatterer himself. Both are true and the book knows it: the flattered man walks into something, and the flatterer is caught by the practice.
Smoothing is the verb, the same one 28:23 used when it said the rebuker finds more favor than the man who flatters with the tongue. Chapter 26 tied flattery to hatred at 26:28 and chapter 27 tied it to the kisses of an enemy at 27:6. Four chapters, one figure, and the book keeps insisting he is not being kind.
Related: Proverbs 28:23 · Proverbs 26:28 · Proverbs 27:6 · Proverbs 26:23
New King James Version®, Copyright © 1982, Thomas Nelson. All rights reserved. Full copyright information. Scripture provided by API.Bible.
Go Deeper
If this verse has been used to put weight on you that it was never carrying, ask about it directly.