The play referred to is "Abhijnanasakuntalam" (The Recognition of Shakuntala) by the great Sanskrit poet Kalidasa, who is often associated with the Gupta period, including the reign of Chandragupta II.
In the play, the character Shakuntala is deeply connected with nature and the hermitage where she grows up. Several plants and creepers are mentioned, but one of the most prominently associated with Shakuntala and her adopted father, Sage Kanva, is the "Madhavi lata."
The botanical identity of Madhavi lata is widely accepted to be Hiptage benghalensis, also known by its synonym Hiptage madablota. This is a fragrant flowering creeper.
The other options are:
Adenocalymma alliaceum (Garlic vine)
Clerodendrum splendens (Flaming glory bower)
Quisqualis indica (Rangoon creeper)
While these are also creepers, Hiptage madablota is the one strongly linked to Kalidasa's Shakuntala.
Hiptage madablota