Possible to own two guilds and link logs?

I am guild leader of Horde Defense League, but we run with a guild on another realm (Shadow Risen - Tich). Is it possible to log raids when running with those guys and somehow link the two?

You can belong to as many guilds as you want, assuming that you have a character in the guild. Alternatively the guild can use manual management instead of battle.net management, and then you can be in the guild without having a character in it.

Is there a way when I log on my main on my Zul’jin toon for the logs to show up for the other guild with whom I am raiding in their log list?

No, but someone in that guild could log it and upload it to their list.