I don't know how far you've gotten in Duo, so it's hard to tell how much detail I can get into without going over your head. The upshot is:
- An infinitive verb is, indeed, placed at the end of a simple sentence. It's placed at the end of the clause in complex sentences.
- The infinitive is not the only verb form that's not conjugated. There are other forms that look different from the infinitive, but remain the same regardless of the person and number of the subject.
- An infinitive verb is not the only form of a verb that can go at the end of a clause.
To get into the details a bit: The form of kennengelernt is the past participle. It's not conjugated according to person so it's a non-finite form. There are three non-finite verb forms in German, the infinitive, the past participle, and the present participle. The infinitive does go at the end of a clause. The past participle goes at the end of a clause when it's combined with another verb as in your example. Past participles can also be used as a type of adjective, in which case they're placed in front of the noun they modify. For example Das Haus hat ein gebrochenes Fenster. -- "The house has a broken window." Here gebrochen is the past participle of brechen. (As I recall, Duo doesn't get into declining adjectives until relatively late in the course, but when used as an adjective the past particle is declined, which is where the -es ending comes from. It's declined according to case and type of noun, not conjugated according to the subject, so it's still a non-finite verb.) Present participles are only used as adjectives and never combined with other verbs, so they're always placed in front of a noun.
Meanwhile, verbs which are conjugated according to person, are placed at the end of subordinate clauses. For example Das ist der große Affe, den ich kennenlerne. -- "That's the big ape that I'm getting to know." In this case den ich kennenlerne is a relative clause, a type of subordinate clause, and the verb kennenlerne goes at the end of the clause here.
The placement of verbs, and which verb form to use when in German is actually somewhat complicated; it depends on the type of sentence, and follows different rules in sentences with more than one clause. You don't have to learn the whole science at once though, and one advantage of using a course like Duolingo is to guide you through the complexities one sentence type at a time. German word order is more flexible than English in general. But German takes verb placement very seriously and if there's any aspect of German grammar that you absolutely must learn to avoid sounding like Yoda, it's where to put the verbs in a sentence.