I replaced a dimmer switch that controls an overhead light in my kitchen. The switch would only turn the light on and off (no dimming capabilities although it was a dimmer switch) The previous owner of my house wired this kitchen so I only know so much from trial and error. When I replaced the switch with the new Lutron Toggler LED+ dimmer for dimmable LED, Halogen and incandescent bulbs I did it incorrectly the 1st time and wired the hot wire to the traveler. There are 2 black wires and one red and I incorrectly assumed red was hot, When I did this the over head light turned on and off and dimmed as I thought it should, but I discovered that the 3 other lights in the kitchen and the overhead light in the bedroom plus the backdoor light did not work at all. I reinstalled the switch correctly (I thought) with hot wire which I confirmed was hot with a voltage tester attached to the black screw and the travelers attached to the brass screws. Now the overhead light will turn on and dim when I toggle the switch and the 3 lights in the kitchen, my overhead bedroom light, and my backdoor light will all turn on, but the overhead light must be off for any of these other lights to turn on. The installation video I watched indicates that it doesn't matter which traveler is hooked up to which brass screw. Is this not the case? Should I reverse them? I should mention that the 2 lights in the kitchen also have dimmer switches which worked before I replaced the overhead light switch, and continue to work when the overhead light is off. Any help that can be provided here would be greatly appreciated. I am mystified.
I only know so much from trial and error
DO NOT do "trial and error". While it seems clever to try combinations until one works, the fact is many combinations will work just fine and then kill you.
Take the time to actually skill up. Just like playing Sudoku, you never guess. Research, measure and think. Know what you have and it will tell you how to wire it.
The 3-way "dimmer" greatly complicates matters. Get it out of there and roll it back to plain 3-way, because the instructions on your new dimmer will instruct you based on assuming you are replacing a plain 3-way.
Travelers are always in the same cable. As long as the cable between 3-ways go direct from switch to switch, travelers are always the same pair of colors.
To answer your question though...
As long as the non-traveler is on the black screw, exchanging the two travelers on brass will simply invert the action of the switch (i.e. with other one down, up is now on instead of down). This is not worth thinking about.
Why not? Because if you don't like the switch action, remove the two screws holding it into the box, pull it out a bit, rotate the switch 180 degrees, and push it back in.