If you let flattery go to your head, it will lead to your ruin.

Literal

Flattery [to-に] carried-[passive-される-と], self [gen-の] ruin [obj-を] invite.

お世辞 'flattery / compliment' uses the polite お prefix. 乗せられる is the passive of 乗せる 'to get someone on board / to deceive' — here 'to be taken in by.' 身の破滅を招く 'to invite one's own ruin' is a formal set phrase. The conditional と marks the automatic consequence. A proverb-like cautionary statement.