Two instruments, the flute and the violin, seem like a perfect match, but surprisingly the repertoire written for these two instruments is a bit more elusive than I thought! Perhaps its the similarity with the range, or the strikingly different tone colors... but whatever the reason, this is an area of repertoire we should explore.
If you are looking for duets just for the two instruments, with no accompaniment, you can poke around in any century. Since both instruments have a long history, they have a vast repertoire. But, the streams didn't cross very often outside of larger ensemble playing.
There are a few examples from Baroque and Classical eras such as the Sonata for Flute and Violin, TWV 40:111 by George Philipp Telemann and the Duet for Flute and Violin H.598 by CPE Bach. These are original works for this pairing of instruments. Here is Hoffmeister's Duet for Flute and Violin in G Major:
However, you are more likely to find even more repertoire if you look for pieces written for "two treble instruments." Telemann did this often, which can open up an area of possibility for this combination.
For the more obscure, try the 6 Duos for Flute and Violin by Campagnoli, various duos written by Alessandro Rolla, both composers active in the early 1800s.
Works with Piano
The repertoire does expand quite a bit when you add a keyboard (harpsichord or piano). Given the treble nature of both instruments, composers really wanted something to ground the music.
If you look for works for flute, violin, and continuo, you will find a vast array of music for this ensemble with composers such as Telemann and Quantz having over a dozen works in this field. JS Bach, JC Bach, and Vivaldi also contributed to the repertoire for this combination. Even Handel wrote a few trio sonatas.
Moving away from continuo and into written out piano accompaniment, JCF Bach's Trio Sonata in C major for flute, violin, and piano, is an early example of this ensemble.
Moving into the late 19th century, check out Carl Hillmann's Serenade and Gondoliera for flute, violin and piano.
A widely recorded modern example of this combination is Nino Rota's Trio for Flute, Violin and Piano (1958), one of the more challenging pieces for the repertoire.
Once you add an orchestra, some more options get added to the list. Vivaldi had several duo concertos for flute and violin, which are typically accompanied by a small string ensemble. Bach's Concerto for flute, violin, and harpsichord is pretty much a trio sonata with an additional string section. Telemann also contributed to the genre with his Concerto in e minor for flute, violin, and strings (TWV 52:e3).
In more modern times, the Concerto for flute, violin, and orchestra by Martinu is often identified as an anchor in the duets genre for concerto literature.
Arrangements and Adaptations
If you want to expand your outlook beyond music written for this pairing, there are hundreds of works that can be adapted.
Music for two flutes translates well for flute and violin. Much of the violin duet repertoire also works, you just have to be wary of parts that dip into the low range of the string instrument.
The Flower Duet from Delibe's opera Lakmé, has been made very popular. Originally a vocal duet from the first act, this has been arranged for flute and violin and has received several thousand views on YouTube.
From baroque to modern, and everything in between, you can find a small repertoire for these two. They may not be overly popular or widely published, but the right people with the right motivation to get these works exposed and more works written is all it will take to uncover even more wonderful pieces for this combination.