Family Tree API
Answers
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The Family Tree app is available to anyone that signs up for a free account.
If you are looking for an API plugin that will interface with reynoldsfamily.org - no FamilySearch doesn't have an api/solution that does that (of which I am aware off the top of my head) - though I have seen a few other genealogy website building solutions out there - I am not aware of any with FamilySearch certification currently.
FamilySearch does have the current capability for you to build a Family Group, to share messaging and social posts about family trees within that group. Maybe implementing that could replace/supplement your website?
FamilySearch Solutions Gallery contains other applications that might be interesting to look at. RelativeFinder for example allows you to discover multiple relationship paths in Family Tree and also has the well-loved family reunion activity Connect with people nearby/Relatives Around Me - which is also a feature built into the Family Tree mobile app (Android or iPhone).
All of the apps I am referring to are free with a FamilySearch login - quite nice!
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FamilySearch does have an API, but several years ago limited access to it to their established partners.
Limiting access arguably was a very good move, because when FamilySearch subsequently released a new and improved GEDCOM standard and began modifying their API accordingly, the established partners' tools all began to break. The partner programmers are all still working hard to keep up with FamilySearch. I know this because I am regularly reporting new broken pieces to their tech support. Basically, what I am saying is your surname study group almost certainly does not want to interface with FamilySearch Family Tree via API at this time. At least wait some years for the dust to settle.
What many surname study groups do, that your group might want to do, is assign one member to maintain a master genealogy database offline in a 3rd party software, and periodically synchronize that database to FamilySearch Family Tree and then from the offline database update their family history website.
Many individuals who do this are members of the Guild of One Name Studies (one-name.org). Recently the Guild added a membership category for descendancy and surname societies. The Guild provides a couple of web hosting platforms and supports others, and supports members in many ways. Currently, the surname Reynolds is not registered with the Guild.
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