"Away in a Manger" is one of the most popular Carols. It was first published in the late nineteenth century.
Here is an arrangement for Flute and Guitar duet. With lyrics and Melody line.
With guitar standard notation and tablature.
Three pages (two pages both guitar and Flute, 1 page Flute)
With downloadable simple mp3 for audio help and practice the Flute.

Deck the Hall  is a traditional Christmas, yuletide, and New Year's carol. The melody is Welsh dating back to the sixteenth century, and belongs to a winter carol, while the English lyrics, written by the Scottish musician Thomas Oliphant, date to 1862.
For Flute and guitar duet.
Easy.
With downloadable mp3's for audio help (one with both Flute and guitar and one with guitar only).
With guitar tablature. With melody line. With lyrics.
Pages: Three pages (score and flute part).

Londonderry Air is an air that originated in county Londonderry, Northern Ireland.
Here is an arrangement for Flute and guitar duet. Early Intermediate.
With tablature. With downloadable mp3 just for audio help. 
With lyrics and melody line. With finger position suggestions.
Pages: four pages score and parts (3 pages both flute and guitar, 1 page flute part), 1:55 min.

Molly Malone (also known as Cockles and Mussels) is a traditional Irsish song.

For Flute and Guitar duet or Flute, Guitar and voice.
With some finger position suggestions. With melody line and lyrics.
With standard notation and tablature. With downloadable mp3 just for audio help.

Easy to early intermediate.
Pages: Three (3) pages (2 pages Melody/Flute and Guitar with tab, 1 page Flute part).

The Wearing of the Green is an Irish street ballad. It is to an old Irish air, and many versions of the lyric exist, the best-known being by Dion Boucicault (26 December 1820 18 September 1890).

For Flute and Guitar duet or Flute, Guitar and voice.
With melody line and lyrics.
With standard notation and tablature. With downloadable mp3 just for audio help.

Easy to early intermediate.
Pages: Three (3) pages (2 pages Melody/Flute and Guitar with tab, 1 page Flute part).