I always think of these as an AD&D creature. Partially because of the quirky 1e monster manual Tom Wham illustration, but mostly because that's what we were playing when I first encountered the creature. They are however, also in the BX rules as well as their nemeses, the displacer beasts.
What is up with that tail?
I think these are an unusual encounter because of their lawful alignment (not generally hostile) and running the mechanics of their short-range teleport ability can be complicated.
Blink Dog (from Cook)
Move: 120' (40')
Att: 1 bite
No. App.: 1d6 (1d6)
One thing that jumps out at me from the stats is that these are pretty tough dogs. They're roughly on par with a dire wolf (B44) in terms of raw fighting ability (a bit less damage on the bite). Despite that, they are skittish (low morale). This probably stems from their lawful alignment and the fact that they are "highly intelligent." It's worth noting that the 1st edition Monster Manual lists them as of "average" INT (human level) and possessing a "fairly complex language consisting of barks, yaps, whines, and growls." (MM10) Whether a DM wants to bring that to his or her BX game is another question, but I personally like the idea of a PC learning the language and having to bark and growl to make themselves understood.
The intelligence level means 1) the dogs can be clever in their tactics, and 2) they may choose to not fight (eg low morale). If you allow for the idea that blink dogs have a language, it's also possible that they could know "PC" languages like Common, Elvish, Lawful, etc. which means parley is possible with good reaction rolls.
Moving on to the blink part of blink dog, these canines can "bamf" in and out during a fight. They do so without error and at random distances (1d4 x 10 feet).
Couldn't write this one without a shout-out to Kurt!
Blinking has two main effects during an encounter. 1) if they have the initiative, the dogs can attack someone and then blink away without allowing for a melee counter attack. 2) the constant shifting of position makes fighting or targeting them very difficult. They also can just "blink out" when/if they decide to flee a fight. They have OK treasure in their lairs, but given that they can teleport away, you might have a hard time tracking them there if randomly encountered.
The exception to their skittishness are displacer beasts. They "always attack" them and they are considered natural enemies. This is less a consideration for typical encounters and more of a delightful bit of flavor that could be mined for plot hooks. I like to imagine that the two creatures' were both initially from some other plane and arrived in the world via some sort of accident or freak occurrence. Both exist partially out of phase with the material world, but it manifests differently for each. Maybe they had some sort of Autobot/Decepticon thing going on. Displacer beasts are semi-intelligent, and they "hate and fear" blink dogs. So the antipathy could be baed upon something more than just competing for space in an ecosystem. Food for thought anyway.
More than meets the eye!