Look up "predicative complement" to understand what is going on here. "Feel" is a "linking verb". Other linking verbs include "to be", "to appear", "to look", and "to seem" (only a partial list). A linking verb ties an adjective to the subject of a sentence. For example: "He seems happy." ("seems" is a linking verb and "happy" is an adjective). "He is happy." ("is" is a linking verb and "happy" is an adjective). "Feeling good" is an adjective phrase anchored by the present participle "feeling". Think of "feeling" as an adjective (not a verb), and think of "good" as an adverb that modifies the adjective "feeling". Grammatically, you should think of the sentences "I am feeling good" and "I am happy" in the same way.

Even stative verbs are occasionally used in continuous tenses, which implies that the state is temporary. For example: -“I’m feeling better.” (Maybe I wasn’t feeling well recently, but now I am) -“I’m living in New York.” (Maybe I haven’t been here long, and/or I don’t plan to stay forever) -“You’re being rude.” (You’re not a rude person in general, but right now the way you’re acting is rude)

Is ‘I’m feeling good’ correct? Since ‘feel’ is a stative verb, how can it take -ing?’ It’s perfectly natural and correct. The ‘rule’ being broken here is too simplified to capture the nuances of real English. I don’t know if it’s still the case, but at one time McDonalds used the slogan ‘I’m loving it!’ What you really need to know about stative verbs is that they CAN describe the present with the ‘present’ tense. For other verbs, the ‘present’ tense is usually the timeless tense.