I checked if I have spare empty Soul Gems of the appropriate size, and I do. I always try to deal the killing blow, but I don't get the captured soul animation nor do I notice my Soul Gems filling up. When I enchant, I use a Black Soul Gem with a Grand Soul inside, and set the Soul Trap effect to '2 seconds'. The Fire Damage effect of Fiery Soul Trap is fixed at 10 pts. The enchanted item gives that purple glow (meaning that it has been enchanted) and its Fire Damage enchantment seems to work fine (enemies are lit on fire).
Note that both weapons already have unique effects but can still be enchanted. Also, in a normal weapon with no unique properties, you don't need the 'http://uesp.net/wiki/Skyrim%3aEnchanting' Enchanting perk (can put two enchantments on the same item) to enchant with Fiery Soul Trap (both Fire Damage and Soul Trap will still work fine).
Is this because the Fiery Soul Trap enchantment's Soul Trap effect won't work properly on enchant-able items that already have unique effects? If yes, is there a workaround for this (other methods, console commands or mods) that can force 'Fiery Soul Trap' to work on these weapons?
Edit: I'm using the mods: http://baldurdash.org/TESSkyrim/USKPFixList.html, http://skyrim.nexusmods.com/downloads/file.php?id=4719 and http://skyrim.nexusmods.com/downloads/file.php?id=6047.http://baldurdash.org/TESSkyrim/USKPFixList.html. My full http://tinypaste.com/f9456e44.