Can I use the Trans-Lentiviral Packaging System to produce virus with FIV-based lentiviral vectors?

No, the Trans-Lentiviral Packaging System will not work to produce virus with FIV-based lentiviral vectors. There are many cis-acting elements that work with the packaging plasmids in the Trans-Lentiviral Packaging System that are specific only for HIV proteins to perform the steps of reverse transcription, integration, RNA packaging (genome encapsulation), etc. If those cis-acting elements are changed to FIV then those steps would not be carried out.