1. He likes growing flowers.
2. He likes growing a flower.
3. He likes growing the flower.
(Are they all in generic use? I mean 'flowers, a flower, and the flower'.)
2 & 3 is not use in generic use because it is referring to a certain flower.
All are grammatically correct, but 2 and 3 don't mean the same thing as 1.
Sentences 2 and 3 would be used VERY rarely because people usually grow plants that have multiple flowers on them.
Yes, all three sentences can be understood in generic use. The use of "flowers," "a flower," and "the flower" in these sentences does not specify any particular flower or set of flowers. Instead, they refer to the act of growing flowers in general.
To determine whether a sentence is being used in a generic or specific sense, you can consider the context and the presence of definite or indefinite articles. In this case, since the sentences use "flowers," "a flower," and "the flower," without any additional context, it can be assumed that they are being used generically to express a general enjoyment of growing flowers.