To suit one's skin (of cosmetics); not to irritate or cause a bad reaction on the skin.
このクリームは私の肌に合う。
This cream suits my skin.
敏感肌だから、新しい化粧品は必ずパッチテストして肌に合うか確認する。
Because I have sensitive skin, I always do a patch test to check whether a new cosmetic suits my skin.
その化粧水は肌に合わず、顔が赤くなった。
That toner didn't suit my skin and my face turned red.
To be compatible with someone or something; to suit one's tastes or disposition; to get along well (figurative use).
彼とは肌に合って、初対面でも話が弾んだ。
We clicked (got along) — even at our first meeting the conversation flowed.
この仕事は私には肌に合わないと思う。
I don't think this job suits me.
あの町ののんびりした雰囲気が肌に合う。
The relaxed atmosphere of that town suits me.