I don't have a Palkia, but if you're trying to complete your Sinnoh dex for a National Dex, go to the top house in Celestic town and talk to the woman. She gives you a picture of Palkia and you add it to your pokedex.
You sir, are the most helpful person I have ever met in my life. This is probably the third time I've asked for this, but I've only been kicked around. When the answer was this simple, you'd think someone would have been kind and pointed it out. Thank you very much, you are a good person.