"나도 끼 부릴 줄 앎" => I can be flirtatious too (if I want to).
* 나도: I also; me too.
* 끼
1. an informal, (street level) talent, flair, or eccentricity for show business, entertainment, art, etc.
2. a special flair or aggressive attitude with the opposite sex. promiscuity.
** It is often used as 끼가 있다, 끼가 많다, etc.
** If the image shows a heart, it might suggest #2 sense, although #1 is more widely used.
* 부리다
1. handle, wield (a skill, talent) - 요술을 부리다, 꾀를 부리다.
2. show, vent (a habit, peculiarity, emotion, etc) - 고집부리다, 심술을 부리다.
* 끼를 부리다: dabble in something, flirt around with something/someone with one's 끼.
* ~ㄹ 줄 알다: know how to (do something). 줄 doesn't mean "line" here but "how to; ability".
* 앎: a noun form for 알다(know).
When used as a sentence ending, it adds an impersonal feel and an emphasis.
- The device works: 그 장치는 작동한다 - a normal sentence.
- "The device: working": "장치(는) 작동함" - more forceful, like a bullet point.