The quote you mentioned, "detachment isn't about not owning nothing, it’s about nothing owning you," is a paraphrased version of a concept found in the Bhagavad Gita, but it is not an exact quote from any specific verse in the scripture.
In the Bhagavad Gita, Lord Krishna imparts spiritual wisdom and guidance to Arjuna on the battlefield of Kurukshetra. The concept of detachment is indeed an important theme throughout the text. Detachment (Vairagya) is often described as a state of being free from excessive attachment to material possessions, desires, and outcomes.
The idea that is somewhat similar to the paraphrased quote can be found in Chapter 6, Verse 9 of the Bhagavad Gita. In this verse, Krishna speaks about the essence of yoga and the mind's nature:
"योगिनोऽन्तर्कृत्य ज्ञानं अशेषेणाधिगच्छति। शब्दब्रह्मातिवर्तते तद्विद्वान् न चान्यद् अस्ति वेदितव्यम्।।6.9।।"
Transliteration: "Yogino'ntar-kṛtya jñānaṁ aśheṣheṇādhigachchhati Śhabda-brahmātivartate tad-vidvān na chānyad asti veditavyam"
Translation: "The yogi who has controlled the mind and senses, and who sees the knowledge (jñana) as distinct from the material world, attains to the highest goal. Such a person realizes the sound of the transcendental Brahman and becomes free from all other knowledge."
Though this verse doesn't contain the exact phrasing of the paraphrased quote, it conveys the essence of detachment and the importance of not being controlled by material desires and worldly attachments. Detachment, as described in the Bhagavad Gita, is about freeing oneself from the dominance of material possessions and desires, leading to a higher spiritual understanding and realization.