The builders of an FDR must comply with DO-178C (the older DO-178B may also be of interest here) as per AC 20-141B issued by the FAA. These documents do not specifically define a data format but provide requirements for what it must be resilient against. Here is an interesting research paper that covers some of the topics you are asking about. Since most avionics use ARNIC 429 as their standard of communication some FDRs provide ARNIC 429 inputs to record the avionics instructions at the time. I would assume these inputs dump the bus data right to the storage medium (most likely solid state memory these days). Since the formats the device uses may be proprietary as well as very low level (and memory efficient) I am sure they make software to dump it to other formats. For example L3 makes a full unit for their FDRs.
After some more searching I found what may be the most comprehensive answer from this Boeing summary document
What Is a Data Frame?
A flight data recorder (FDR) data frame is the order of the words that are transmitted from the digital flight data acquisition unit (DFDAU) to the digital FDR (DFDR) each second over many seconds (see ARINC 717 for additional information). Most FDR system data frames are made up of four subframes within one superframe. For a 64-words-per-second (wps) FDR system, a DFDAU will output 64 12-bit words to the FDR each second, where each word typically contains the value of an analog parameter. The order of the words (for example, word number 12 of the 64 words) within a subframe, as well as the order of the subframes, define an FDR data frame. This order is important to understand in order to decode the data recorded in the DFDR.
It should also be noted although they may have all been phased out by now, some older cockpit voice recorders and FDRs recorded on analog mediums and may still be inservice doing so.