"We are all just prisoners here, of our own device"

In that line, device means:

2. A project or scheme, often designed to deceive; a stratagem; an artifice. Source: Wiktionary

In other words, the song is saying that we are all prisoners by our own means. We weren't tricked into this situation by anyone else; if we were tricked at all, we tricked ourselves. Our own plan put us where we are.

As noted in a previous answer, device can mean a "project or scheme ... a stratagem; an artifice," whence a "prisoners by our own means" interpretation.

That general idea is almost certainly correct, and own device is sometimes used that way, but (examining some references from ngrams) one finds that own device is frequently used with its "piece of equipment made for a particular purpose" meaning, while own devising more frequently refers to strategems or plans made by oneself.

In the subject lyrics, the context is

The pink champagne on ice
And she said "We are all just prisoners here, of our own device"

which suggests to me that the Eagles used device rather than devising to get the rhyme with ice.

I think the definition of device from AHED applies:

device, noun: A contrivance or an invention serving a particular purpose

The line means we are in a prison of our own making; we devised it ourselves.

device here is a metaphor for "your own doing". so it means here that we become prisoners by our own thoughts and our own actions... hope that helps!