If you're kicking properly, the rate at which you kick should be tied to your stroke rate. That is, every time you take a stroke and rotate your hips and shoulders, your legs should finish the movement as a kick.
This is what's known to competitive swimmers as a "two-beat kick." In one full stroke, you kick twice, once with your left foot and once with your right, as you rotate from side to side. The kick is really just finishing the stroke. For shorter-distance sprint swims, there's a high-frequency kick known as "six-beat kick" where you kick once to rotate, then scissor kick with both feet, and then repeat on the other side.
For any sort of distance swimming (200+ yards) a two-beat kick is really what you're looking for, otherwise you'll be burning energy through your legs, which don't really help much with propulsions. But it's important to remember that kicking should never be about flailing you legs faster and faster. Your kick should fit in with your stroke rate and body rotation, either one kick per rotation or three.
As you slow down when you're swimming, it's usually because your stroke rate has slowed down. You aren't taking strokes as quickly and your body isn't rotating from side to side as frequently.
I see lots of lap swimmers who jump in and kick aggressively for the first few minutes with a high stroke rate who then slow their kick down and their stroke rate slows as well. Keeping a focus on your kick can really help you maintain a constant stroke rate and keep you moving along for workouts or distance swims.
For more information, check out the swim program I'm running called Online Swim Trainer. Hope this helps!