Hi Darío, here are some references on the production and perception (but not acquisition) of American English flaps.  

Production:

Fukaya, T., and Byrd, D. 2005. An articulatory examination of word-final flapping at phrase edges and interiors," Journal of the International Phonetic Association  35, 45-58.

Warner, Natasha, and Tucker, Benjamin V. 2011. Phonetic variability of stops and flaps in spontaneous and careful speech. Journal of the Acoustical Society of America 130:1606-1617

Perception:

Horna, J. E. 1998. An Investigation into the Acoustics of American English Flaps, with a Secondary Emphasis on Spanish Flaps, in Fluent Speech. Ph.D. dissertation, New York Univ.

Warner, Natasha, Fountain, Amy, and Tucker, Benjamin V. 2009. Cues to perception of reduced flaps. Journal of the Acoustical Society of America 125:3317-3327.

Bettina, thank you for your feedback. I wasn't aware of Horna (1998).

Hello,

See the following:

Klein, H. B., Altman, E., & Tate, J. (1998). Relationship between perceptual and acoustic judgments of children's flap productions. Contemporary Issues in Communication Science and Disorders, 25, 25–31.

Klein, H. B., & Altman, E. K. (2002). The acquisition of medial /t, d/ allophones in bisyllabic contexts. Clinical Linguistics and Phonetics, 16, 215–232.

Have fun!

lk

Sorry, two more:

Rimac, R., & Smith, B. L. (1984). Acoustic characteristics of flap productions by American English-speaking children and adults: Implications concerning the development of speech motor control. Journal of Phonetics, 12, 387–396.

See also

Zue, V. W., & Laferriere, M. (1979). Acoustic study of medial /t,d/ in American English. Journal of the Acoustical Society of America, 66(4), 1039–1050.

Thanks a lot!

DBP

You can find phonetics books dating from the 1930's on flaps.  Gleason's outmoded text explains them. What nobody seems to mention is that British English uses the same flap as American does, but their flap signals a medial  [r], whereas the American one signals a medial [d] or [t].

Elaine, thanks for your feedback. The Brit Eng flap can sometimes signal /r/ (a bit old-fashioned pronunciation, though), but as you know in the UK /t/ is increasingly becoming flapped (see e.g. Hannisdal, 2006). I posted a previous query in The Linguist List for t-tapping in Brit Eng and didn't receive much feedback.

Reference

Hannisdal, B. (2006). Variability and change in Received Pronunciation: A study of six phonological variables in the speech of television newsreaders (Unpublished doctoral dissertation). University of Bergen, Norway.