The chair is either Jacobean revival or Spanish revival and the (I think it's a vanity table) is French-y.

They could go together if you have a mix in the entire room, but as a pair, you are right, they aren't the best combo.

I would take the desk and it would be easier to find a chair that has the cabriole or some sort of tapered leg on it. Or, you could do a contemporary desk chair as long as it had some delicacy to it.

No, I wouldn't put them together. I'd pick the chair because it can be a stand-alone piece off to the side or in a corner until an appropriate desk is found. But I'd love to see it paired with something really minimalist and sleek, like the tops and legs you can put together at Ikea. It looks like the seat cushion may be an afterthought and could be replaced with something better, but I do like the high contrast.

I'd go with the desk as they are harder to find and I like the style of this one.

Chairs are much easier to come by.

The desk has Queen Anne feet so something more colonial/traditional would work with the desk.

Definitely the desk. It will be so much easier to find a chair to pair with it than to find a desk to pair with the chair.

They don't work together, but if they are both reasonably priced, and you have space to use them separately, I'd get both.

I love barley twist furniture like the chair. Look at the prices on some on eBay at the link below, and you may have found a bargain. I think I see a tiny hole in the cane work on the back of the chair, near the bottom, but it may be just the photo.

Here is a link that might be useful: Barley twist chairs on eBay

i definitely prefer the desk and would pair it with either a chair similar to what annie pictured or a traditional desk chair- with wood and leather or upholstery on casters... but, can't tell if that piece is large enough for a traditional desk chair- it would prob have to be smaller scaled. i like castered chairs at desks!

the chair could look interesting if someone did something really funky with it paint and fabric wise, but that's not my thing...

I have a piece of furniture similar to your desk, it came from my moms home and she used it with a bench and had it as a vanity in her bedroom.
I now use it in my LR and do not use the bench.
It might be awkward as a desk if you spend many hours their. But if just for the occasional use it will be fine.
I think a regular chair will be too tall but you can only tell by going to see it.
If the price is right it is a lovely piece.

I would say they are BOTH beautiful but what would you use more? Also, What other wood tones/colors do you have? If you have darker furniture grab the chair, lighter grab the desk/vanity.

I love both pieces but if I had to choose just one it would be the desk.

I think they can go together in an "eclectic sense" if your room is eclectic.

First of all, thank you for the many responses and opinions.

Pal, I googled Jacobean revival furniture after reading your post, and one of the first articles I read said to avoid buying the chairs because they won't be comfortable. lol

Just to give you all an update, I went to see both the chair and the desk tonight. Take a moment to ponder the improbability of my getting first dibs on any Craigslist find. It never happens. Anyway, the desk is very nice, very graceful, good bones, and I bought it immediately. An interesting note about it is that it's from a Scottish furniture maker, Beithcraft. Would love to know how it got over here. The middle section isn't as low as it appears in the picture, and it's about the same height as my current computer desk so I think I could find a chair to fit it. Thank you all for the suggestions on what to pair it with. The pic from Annie was very helpful. After getting it home, I'm not sure I'll even try to make it a true desk. I put it in a spot I was saving for a trestle or library table, and I think I might use it in the same way. It would be a shame to plunk a computer and all its ugly parts on that wood, which is in great shape.

The chair OTOH I decided to pass on. Good eye, my3dogs! There was a bad spot in the cane on the back. Not broken, but probably heading that way. And although I could have lived with that, the cane in the seat was loosey goosey to the touch, and I'm looking for a functional chair. It's a shame, because I love me some barley twist. So I didn't get the desk or chair I was seeking, but I got a lovely piece of furniture at a great price.

Thank you all again for helping me out!