The following is a technique that is not used allot but is very accurate and flexible to accomplish what you want. The apparent reason for its lack of common use is that many people fear or are ignorant of how to use xml technology. FileMaker uses xml natively all the time. Given your intentions for the bidirectional flow of data/content this might be a way to achieve success. It does require some work, but the vehicle (xml) for the data flows is proven, reliable, and available to all three client application products you mention (InDesign, Word, and FileMaker).
If I understand the process you described is (InDesign -> Word -> FileMaker -> InDesign ---to complete the circle of "data" life).
Not knowing why you need the Word in the loop, other than there appeared to be a way to step the data through that product - which is perfectly valid.
You might be able to take it out of the loop, again depending on what actions you have planned for Word to do, by performing or asking the indesign data provider to perform an xml export process. If you want consider this approach to/from InDesign using xml technology see XML
If Word provides a necessary role/step in the process, most ms office components, including Word and Excel, may simply "Save as XML" - you would then need an xslt (see below) for FileMaker for each unique structure to be integrated.
XSLT - The most technical step required is the I/O import export of the FileMaker database. Getting the data into your platform of choice for update (FileMaker), using this method, requires the creation of an xslt (xsl transform - for lack of a better description it is a file that provides programmatic instructions and translation for an "intelligent/controllable" import of data into filemaker). It requires some analysis of the xml result from one of the two data source methods described.
Streaming the data out or export provide for a myriad of methods and available plug-ins as well to push the data directly or indirectly into InDesign.
FileMaker being highly popular in the design and publishing arena there are likely to be other responses here for you to consider.
Obviously the short answer to your question is YES!
Thanks for the detailed response. And apologies for the delay in replying. Been away on family holiday. Word is not crucial to the process. I only mentioned it as last year's setters sent me the para tagged Word file when I asked them about exporting options. I'm happy leaving Word out of the loop, so we would just have InDesign -> FileMaker -> InDesign. While I have a working knowledge of both applications, XML is something I have not delved into before. I am sure I could teach myself, but I am not sure I can do so in time and it might not be the best use of my time. So I am open to bringing in someone to do this for us.
If this is a service you, or other readers, can provide on a professional basis then please do contact me off this discussion board. My contact details are available on our website www.toynbee-editorial.co.uk
I will contact you.