If you ask “Where can I find any flea markets/vintage stores in Antalya?” for vintage shopping there are tree different places you may go:

Kaleici Old Town

This is the old town in Antalya and it is totally worth the visit.  Easy to find such authentic places, friendly cats,  traditional vintage shops and instagramable shots in the town.
And it is place to have a great walk with your family and to stop to have some tea in the local cafes.

Kaleici Old Town Antalya

Sobacılar ve Bakırcılar Çarşısı (Bazaar of  stove producers and coppersmiths)

BAZAAR OF SOBACILAR AND DEMİRCİLER

Sobacılar bazaar is place  where mostly vintage Turkish handmade cupper  tools and stoves are available

Region of Hans (Hanlar Bölgesi)

Region of Hanz in Turkish Hanlar Bölgesi  is place for clothing. You may find vintage  shoes or dress, etc.

HANLAR BÖLGESİ Antique Bazaar