I've been a semi-audiophile and a musician for... way too long now, and I have heard a lot of headphones in the $10-200 segment, both good and (mostly) bad. I'm always looking for good bargains in phones, and decided to check out the Flats along with several other closed-ear JVC models in the same price range. I came away pretty impressed with these little guys.
Note the "foldable" Flats do not appear to be "fully foldable" a la the Sennheiser PX100s; the earcups simply rotate 90 degrees, "flattening" the phones. This definitely does save some space for travel, but there's still going to be a significant footprint taken up in your carryon bag.
As far as I'm concerned, the phones to beat at this price point (and several points above, besides) are the Koss KSC75s. These phones have a sense of spaciousness, sweetness and detail that is frankly absurd for their price. The Flats, priced very comparably to the KSC75s, are still no match for them. However, unlike the KSCs, the Flats are a closed-ear design, so they do provide better isolation both for the listener and the listener's nearby compatriates. It's impossible to use the KSCs on an airplane; the Flats would probably fare at least somewhat better in that context.
So the Flats are probably best compared instead to phones like the venerable Sony MDR-V150. The 150 is a basic, cheap, small closed-ear phone at the same price point, and until now I've known of few others of similar design / price to recommend to folks wanting a semi-portable closed-ear model for a Jackson or so. The Flats definitely have much more character and sweetness in the midrange than the 150s, and I would recommend them over the Sonys for this reason alone. They also seem to have a little more low-end extension and sound a bit less "synthetic / plastic" down there than the 150s do.
Comfort may be an issue for some with the Flats, as mine seem to press unpleasantly (but not intolerably) on the bottom of my ears through the cups; because of this I've yet to forget that I'm wearing phones, as I often do with my KSCs. However, phone fit is very personal. It's worth mentioning that I have a (literally) big head.
Interestingly enough, I have A/B'd these with JVC's larger closed-ear models the HA-RX300 and HA-RX500. The RX300 is all bass and I can't recommend it to anyone who's successfully completed adolescence (unless you're thinking about buying Beats, in which case you ought to save yourself several hundred bucks and get the RX300 instead). The RX500 is much more well-balanced and I can see why people like it at its price; it's a full-sounding, reasonably accurate (if rather excitement- / personality-free) set of phones. The comparatively tiny Flats have most of the bass response of the RX500, but noticeably more sweetness and personality... although the RX500 is way more comfortable.
Summing up, if you need a set of portable closed-ears and don't have much to drop on 'em, this is probably where you ought to start. There are better choices sonically at the price point... but not very many.