Off the top of my head it can be heard prominently in the "Eve no Jikan" soundtrack from 00:00 and in Fat Freddy's Drop's "Breakthrough" starting at 2:34 or so, though I have definitely heard it in other places too. Is this a real instrument and what is it?
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The intrument playing during the intro of the Eve no Jikan work is a Mellotron. This was an early keyboard sampler instrument that used one length of magnetic tape per note, with one playback head for each tape. Depressing a key on these instruments started a process whereby the length of tape (totalling around 8 seconds of playback) would start moving and the playback head for that note would be engaged with the tape. Melltrons were commonly manfactured with sets of tapes of flute, cello, violin, vocal and brass samples. Some more complex models also came with a second keyboard which was matched to tapes of sound effects, pre-recorded drum patterns and basic backing tracks recorded by studio musicians in a variety of styles. The Mellotron was devised, in part, to allow people to entertain guests with basic one or two-finger playing; reproducing the rich sounds of Tiki Bar-style Exotica music or lounge jazz. And all with only a rudimentary conventional keyboard technique.
On the first example, the Mellotron is configured to play the 'flute' bank of tapes within it. This is the same setting used notably on the intro to Strawberry Fields Forever by the Beatles. It can also be heard in 'A Punk' by Vampire Weekend.
Rather than simply playing back an identical tape at different speeds, Mellotron tape banks consisted of uniquely recorded tapes for each note. As such a C# tape consisted of a unique performance of a flautist playing that note. Because these are electromechanical instruments, holding down a key kicks off a series of processes. This gives the notes themselves an artificially hard attack and decay; especially on Mellotrons in need of a service.
Part of the charm of Mellotrons is the fairly idiosyncratic timbre and warble that each note has. When used live by progressive rock bands such as Yes and the Moody Blues these instruments had a tendency to drift out of tune, or break down entirely. As such they were replaced with analog and digital synthesisers over time, and were viewed as obsolete for many years. Fortunately for the Mellotron, the dirt, warble and general synthetic tone of them has become popular again. The sounds of the Mellotron are used quite commonly where a nostalgic or ethereal tone is required. They don't sound like real flutes or strings, but they don't sound like digital reproductions either. As such they have quite a ghostly quality.
Due to this reliability issue, many keyboard and synth players use emulations instead. Some Nord keyboards offer reproduction Mellotron sounds. There are also soft synth emulations available, and you can still purchase Mellotron-branded digital keyboards. It is likely that in both examples posted above, samples of Mellotrons rather than the real instruments were used. In the case of the Fat Freddy's Drop track, the sound isn't exactly like Mellotron flutes, but is clearly an approximation designed to evoke the same sort of aesthetic and texture to the music.