The industry standard format for sharing GPS data is a GPX file. Gaia GPS can export GPX files, and Goat Maps can import those files.
If you have a small number of tracks you can export them one at a time from the app or website. If you have a lot of data saved, the best way is to email support@gaiagps.com and ask them to export your account. After a few days you should receive an email with a link to download a zip file containing all your data.
Once you've got your zip file, follow these instructions to learn how to import it into Goat Maps.
Goat maps does not currently support photos, so photos exported from Gaia GPS cannot be imported into Goat Maps.