It looks like both .flb and .fmp3 files are used by FileMaker Pro and thus if any program could somehow (if even) convert them, it would be this program. However, we haven't found any specific information about this conversion, if it actually works somehow.
Convert FileMaker Pro label file to FileMaker Pro for Mac document file.
We have found 2 software records in our database eligible for .flb to .fmp3 file format conversion.
Microsoft Windows software - convert flb to fmp3 on Windows
A program used to create and manage information databases
Convert from flb file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned flb to fmp3. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
Apple macOS / Mac OS X software - convert flb to fmp3 on OS X
A database management program for Mac