I agree. "I like to learn" seems like it'd use the infinitive "lesen." But since "lerne" is definitely conjugated for the first person singular ("I learn"), and since "gern" is an adverb, I think "I learn happily" should certainly work.
Is there a reason why it wouldn't?
Well, "I like to learn" is the better translation, closer to the meaning of "Ich lerne gern".
"I learn gladly" suggests you are actually learning (which the German original does not) - the grammatical construction should be none of a translator's concern.
When you say absolutely the same thing in Italian, it would be "Mi piace apprendere" and you should NOT translate this with "It pleases me to learn"
I am finding that I am learning on two levels: what the words really mean and what Duolingo will accept as a translation. As a long time programmer I can guess the technical difficulties they must have with acceptable translations, but that doesn't make it any easier. I just trust hope that the accepted translations are valid also and go with that.