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Dear Mr. Salmon,
A search for the Florida East Coast Railway in the National Archives Catalog brings up the following results. Information on contacting the respective NARA units holding these records can be found at the bottom of each catalog entry.
Additionally, searching for the railway on ArchivesGrid will give you a list of repositories throughout the country that hold related records. You can see the results of this search here, including collections at the Library of Congress and the University of Florida, among others.
Best of luck in your research, and thank you for using History Hub!
If you have not already done so, you may wish to review Reference Information Paper 91 - Records Relating to North American Railroads. It can be freely downloaded at https://www.archives.gov/files/publications/ref-info-papers/