(1) Almost all native speakers tell learners not to use the present progressive with verbs such as "like," "love," "hate," etc.
(2) In other words, if someone asks, "Do you like me?" don't answer: Oh, yes, I am liking you very much.
(3) BUT there are exceptions to every rule.
(4) I like = I like something: I like to study languages./ I like you./ I like watching TV./ I like nice people.
(5) "I am liking" is now "good" English if you mean that you are developing more and more an affection for something.
(a) Tom: Do you like me?
(b) Sue: Well, when I first met you, I did not like you.
(c) Tom: And now?
(d) Sue: I am liking you a lot now (more and more each day). In other words, her "liking" for him is growing.
(6) Learners, however, probably should use only "I like" until they understand English well enough to use "I am liking."
(7) No doubt you will hear "I'm liking" in American movies and TV shows.