Flyspray is not actively tested with Windows Server IIS. Last time I tried in a VM in 2019 with Flyspray 1.0-rc9 it seemed to work.
Usually do when moving to other server:
1. Backup the database that contains Flyspray data. For instance with mysqldump when you used MySQL.
2. Backup attachments/ and avatars/ folders of Flyspray installation as attachments and profile images are not stored in the database.
3. Look how the IIS setup was done in the old server and mimic it on the new server?
4. Install/Configure PHP for IIS and install Flyspray there.
5. unzip attachments/ and avatars/ folders from step 2 inside Flyspray directory.
6. Adapt some directory restrictions from Apache/.htaccess to IIS configuration. This has probably not done anyone officially, search Flyspray sources recursive for .htaccess and htaccess.dist files to get an idea.
7. Install and configure your database on the new server. For instance install MySQL if you used it before there.
8. Put the old flyspray.conf.php to the new server and adapt it to the new server.
I found a screenshot I made in 2019 that at least showed it worked:

environment.