Yes, 'flirty' is an adjective; it describes a way of behaving
which is playful, teasing or superficially friendly, with amorous
overtones. For example:
Conversation between the acquaintances seated together was light
and flirty.
She is a natural flirt; her manner when meeting people she likes
is flirty.
'Flirtatious', also an adjective, means the same as 'flirty',
while 'flirt' - meaning a person who flirts or is flirty - is a
noun, and 'flirt', meaning to be flirty, is a verb.