When you start getting advice about where to do a post-doc, most faculty members will tell you, "Do the best post-doc you can with the best mentor." This is very sound advice, but I haven't yet found it actually helpful. There are lots of kinds of post-docs out there, and as someone who is currently looking for more specific experience in a post-doc, I need more guidance. So I keep doing what has proved to be so helpful in my career/job hunt: I keep asking people.
One of the people I has a chance to sit down with is and FDA PI that I met at a scientific meeting. He had an abstract in the meeting book, but when I suggested his job must be a lot like working at the NIH ("C'mon, you get intramural funding, right?"), he gave me a look reserved for the naive and offered to explain it to me.
Yes, as a PI, he runs a lab with scientists who work on projects and publish in peer reviewer journals, and yes, they are funded intramurally. As an FDA scientist, his research tends to be on important issues of public interest that either aren't high impact or narrative driven enough to be performed by either academic or industry scientists. For example, recently, he tested whether the naked DNA in vaccines can be incorporated into cells, and whether this was a risk factor for transformation. He holds his lab to a similar standard as other high functioning labs, they publish about 1 paper/person/year, (although he says it might be hard to move to a faculty position afterwards because there isn't usually a defined project to take with you).
But, that is just a portion of what he does, his other major role at the FDA is to be the guy on study sections where the data from clinical trials is weighed for FDA approval. Companies think they've found a miracle drug, collect a decade or so of data, and then the whole giant pile (imagine him, holding his hand a meter off the ground to demonstrate) gets sent for review to people like him. They read through it, both to make sure that all of the appropriate experiments have been done and regulations met (and he will ask for more if something is missing) and to think very critically about the science. Much like being a program officer, the FDA trusts that the best reviews come from someone who is actively doing research (although there are also people who do full time review with no bench component). This is a severe peer review, and because the stakes are so high, he is really passionate about the role he serves in this important but bureaucratic process. And, he told me, they need more people in these roles- if you post-doc at the FDA, you get some training in how to read these types of documents and make recommendations- the regulatory science aspect. As PIs tend to do, he made it seem straight-forward to transition from a post-doc to a staff scientist position that would have a regular commitment to the regulatory aspect of the job. He likes the dual nature of his job, he goes to both science meetings (where I met him) and regulatory science conferences, and sends people in his lab to both as well.
How can you pursue this type of job? If you want to enter as a post-doc, the usual post-doc route is open to you. Investigate the PI of interest, send them a letter and start a dialogue. It probably would help for you to be clear about your interest in learning about regulatory review. I've just run across this fellowship program for research/review training in oncology, there may be others like it for different broad fields. This particular program is for those with 3 years of post-doc experience, and the fellowship program suggests you will "develop skills of value to academia, the pharmaceutical industry, and government agencies." And this was his main complaint (although you should see it as an opportunity), the people who get trained to read these documents at government wages tend to get lured away to write them at drug company wages.
Here is a list of the many FDA opportunities, for everyone from current students to research faculty. I'll point out that a lot of these positions are in Washington DC, but there are some at the Oak Ridge National Labs, and I've seen various FDA jobs pop up all over the country on USAJobs (particularly inspectors).