Linux has no problems at all with the FAT32 filesystem - in fact, it's very common to use a FAT32 partition to share stuff between a Windows and a Linux installation.
In order to access ANY filesystem or partition, you'll have to mount it (for details, see the man page for mount). If FAT32 partitions are detected during the Slackware installation, one is asked if one wants to mount them (and if so, to specify the mount points). That information ends up in /etc/fstab. However, the FAT32 partition will be accesible only to root/su by default. This is easily changed by making the appropriate changes in /etc/fstab. Some more extensive information on this topic is available at
Simply Linux, and I think there are some tips at
user local as well...and of course, there are loads of discussions on this topic on this very forum.