Been riding stock 25c Kendas from my Motobecane Track with light skidding for more than a year, they are just starting to wear out. I've gotten a couple pinch flats and other flats from road debris, but nothing out of the ordinary.

Lady's been riding stock 23c Kendas (the same ones OP is riding, I think) for about a year with light skidding and she's never gotten a flat, but they're obviously not as durable for le skidz since they're marketed as "light" tubes.

If you like skidding, I recommend the cheapest rear tire you can find. I just picked up 2 lightly used (~50 miles) CST 25c tires for $5... perfect candidate for skidding.