We present the largest and most spatially extended planetary nebulae (PNe) catalog ever obtained for the Fornax cluster. We measured velocities of 1452 PNe out to 200 kpc in the cluster core using a counter-dispersed slitless spectroscopic technique with data from FORS2 on the VLT. With such extended spatial coverage, we can study separately the stellar halos of some of the cluster main galaxies and the intracluster light. In this second paper of the Fornax Cluster VLT Spectroscopic Survey (FVSS), we identify and classify the emission-line sources, describe the method to select PNe and calculate their coordinates and velocities from the dispersed slitless images. From the PN 2D velocity map we identify stellar streams that are possibly tracing the gravitational interaction of NGC1399 with NGC1404 and NGC1387. We also present the velocity dispersion profile out to $\sim 200$ kpc radii, which shows signatures of a superposition of the bright central galaxy and the cluster potential, with the latter clearly dominating the regions outside R $\sim 1000$" ($\sim 100$ kpc).