The answer to Phil's question seems to be "It's complicated" But my understanding is that the seven kings are seven Roman emperors. I'm not sure exactly which ones. There is a similar vision in 4 Ezra 11-12 of the Eagle and its three heads and twelve wings. The twelve wings are Roman emperors. Again there is debate on exactly which ones.
For notice of previous posts in Phil's series on Revelation, see here and links.
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