The problem isn't within the toaster, and adding a "power conditioner" wouldn't help. It's simply drawing a lot of power from the outlet, and the wiring impedance between the outlet and the distribution panel is causing the voltage at the outlet to drop a bit.
In general, the lighting circuits and the countertop appliance circuits should be on separate breakers to begin with, so that an appliance fault won't leave you in the dark with a potentially dangerous situation (hot and/or spinning objects).
You should try to work out which outlets in your kitchen are on which circuits, and operate the toaster on a separate circuit from the one your lights are plugged into.
Some LEDs with switching power supplies demand power in pulses, which can get coupled back onto the power line as small surges. If you have bulbs which are making that demand at different frequencies, and the current available is a bit marginal, this can sometimes make one or more take longer to charge than they should and cause flashing.
I have a chandelier which takes 16 bulbs, which is something of a worst case since they are all trying to draw power through the same ten-foot lamp cord and am using a dimmer to control its brightness. When ask the bulbs were identical, there was no problem. When one failed and I replaced it with a bulb that drew a tiny bit more power, some dimmer levels would cause that new bulb to flash badly. Replacing it with a bulb that drew slightly less power than the others solved the problem. I have some guesses about exactly why, but they are more detailed than I think we want to into here.
So I'd try making sure all the bulbs are identical and see if that helps.
Some folks have reported that replacing one of the bulbs with an incandescent or fluorescent may also solve the problem, since these draw power differently. Again, I have some guesses about why, but they are mostly guesses. Might be worth trying an experiment, though.
We're playing with a product that's still in the early stages of its evolution. There are likely to be a few hiccups before the manufacturers learn how to make them "as cheap as possible, but not cheaper." I am trusting/hoping that those companies are aware of this effect and will solve it eventually. Unfortunately, given the long life of LED bulbs, that may not help us early purchasers very soon.
Best Answer
Dimmers have to be compatible with the types of lights in use. The bog standard dimmers that have been in use for years generally work fine for incandescent type bulbs and the halogens that work at direct line voltage.
With the advent of CFLs (compact florescent lamps), low voltage halogens and LED types it talks special types of dimmers for these to be used in a variable brightness mode. Do note that not all items are even dimmable and you can get into serious overheating issues in either the dimmer switch or in the light module if you try to operate with a dimmer. Similar issues can happen when a non-compatible type of dimmer is in use.
My suggestion for you, if you need to keep the mix of light source types, is to convert over to simply using a switched on-off control instead of dimming. If dimming is desired then switch all of the light sources on the circuit to the same type and then select a dimmer that is compatible with that type of lamp. Modern dimmers should show on their box what types of lamps they should work with. In the realm of the light sources themselves you may need to do some additional research to determine if a particular low voltage halogen, CFL or LED lamp assembly is actually dimmable. It may come down to specifically only purchasing items that are marked as dimmable on the box or product information sheet.