Although it's generally easier to land an academic and clinical job in the same area than to land dual academic jobs, clinical jobs and most clinical post-docs won't follow the same timeline that you'd be on while applying for academic jobs. Unless you get something in writing for two jobs at the same institution, chances are you'll have to decide on a job offer before knowing for sure a job will be in place for your partner.
Of course, you can have a sense of the prospects of jobs for your partner depending on the area, different settings your partner is interested in (e.g., state hospital), how far either of you is willing to commute, etc.
My partner and I were lucky enough to get dual academic jobs (whole other story in itself), and my biggest piece of advice is probably pretty obvious: be as supportive and honest with each other as possible. It's a stressful time for sure with all the uncertainty. At the same time, you both need to be honest about the types of jobs you want as well as the ones you can accept. It's one thing to accept a job that's less than a perfect fit for the sake of your partner. If you talk yourself into a position or location you know you won't be happy in, though, you're setting yourself up for more stress and the likelihood that you'll be back at Square One trying to find jobs near each other again.
Also, I'd recommend your partner research possible post-doc/clinical opportunities in an area once you receive a phone/Skype interview invitation (I'm referring to post-docs outside of formalized ones with specific deadlines; of course those will need to be researched well in advance!). Timelines vary, but that should give enough time to get a sense of job prospects in general, to reach out to any colleagues in the area, etc. Waiting until a campus interview or job offer doesn't give you enough time, and if you're applying all over the place, it's overwhelming researching every single area an application is going to. Cast a wide net if you can.
My partner and I also shared a spreadsheet with job applications and deadlines so that we could see whenever our searches were overlapping. This also made a quick look at job prospects for desirable jobs for the other partner easier once one of us got a job interview.