We already have the Minmatar grenade, a brute-force concussive blast.

We have the Caldari grenade, the Flux, likely made to counter and control Caldari dissendet groups that would be using Caldari technology (since they're heavy shield tankers).

For the Amarr grenade, I say it'd be a thermal grenade. In EVE fashion (like the Caldari above), it's most effective against those that use it. It'd do a blast of thermal damage to shields and armor, and also instantly overheat any weapon that has an overheat mechanic (Laser Rifle, Scrambler Rifle, HMG, Rail Turrets, Blaster Turrets), thus incapacitating them until the weapon cools. Would be effective in temporarily incapping vehicle and installation turrets, would take HMGs out of the fight for 5 seconds (they have a long and rather awesomely animated cooldown), and would do bonus damage to anyone using a Scrambler or Laser rifle as the weapon overheats and gives feedback damage.

For the Gallente, I couldn't come up with anything but some sort of ECM grenade. The Gallente command ships in EVE give bonuses to Electronic Warfare, and so the gallente grenade wouldn't do any damage, but could remove/fizzle the HUD, removing the Radar, all those helpful symbols, and the weapon crosshairs while hip firing (ADS would be uneffected). Since it'd do no damage, it could even have a rather large blast radius.

AV grenades are they're own special snowflake and I don't see a reason to introduce more variants of those, so the Caldari can just have 2 grenade types.

Thoughts?

I like your ideas.
For the AMARR, the effect of overheating should last 2-3 seconds. 5 is way too much. Though if affected with 2 or more time could accumulate.

The 5 seconds was just for the HMG, because around that is what it's actual cooldown time is if you overheat it. For my idea, the grenades just overheat the weapon, and how fast it cools down depends on the weapon's cooldown time + any skills the affected player as that effects cooling.

Well, you got the racial flavors a bit switched, but otherwise its a good idea.
Think about it this way, amarr ships deal primarily EM damage, which is the most effective at cutting through shields. That sounds like a flux to me. Minmatar are explosive, Caldari are kinetic, and Gallente are thermal. Those are their historic racial damage variants.