Ok so my advice is.
Train Espeon, A LOT. You can take care of Will, Koga and Bruno just with it if it's fast enough and highly leveled.
For Karen, Use Typhlosion against Vileploom, Umbreon, and Murkrow. Espeon for Gengar, Donphan for Houndoom. You can also use Electric type for some of them as long as its not weak against them.
You definitely need something Electric to get rid of Lance's Gyarados asap or otherwise it's keep beating the crap out of you.
Use Electric type for Aerodactly as well cos it has Thunder fang and will beat your water type. Also either strong Rock type attack or Electric Pokemon against Charizard.
Now, three Dragonites. I needed a lot of Draco Meteors and Blizzard/Ice Beam's to beat them. A strong Ice type is the most painless way but it has to be quick and strong or you'll need a lot of time and revives and full restores. I personally had a lot of luck with Haunter's Hypnosis but that's pure luck.
For Electric type, it'd be a really good thing if you could get a Jolteon cos its quick and has a great Sp. Atk which is what you need :)
As for the other League members, most of them are weak against Espeon, but you should check Bulbapedia and see all the Pokemon they have and combine which Pokemon you'll use and when :)
Feel free to hit me up with a PM if you need any more help.