There is currently a possible bug with the Killstreak Fabrication Kits (Specialized and Professional). You can apply Killstreak Kits to Strange Items, but you cannot use the results in the Upgrade kits. You can see an example below.
As you can see in these two screenshots, I have both a Strange Killstreak and a Unique Killstreak Direct Hit.
When I try to use my Specialized Killstreak Direct Hit Fabricator, it does NOT accept the Strange Variation, only the Unique.
This MAY be intended, as the Killstreak Item used in the recipe is LOST upon craft. You can also use the Killstreak Weapon in ANY Fabrication kit. it is not limited to the original weapon used.
Also note that the Killstreak Path is not a direct one. You can take a Unique item without any Killstreak bonuses, and use a Professional Kit right on it. If you want to upgrade an Existing Killstreak Weapon with a new kit, you first need to Restore (remove) the existing Killstreak application.
I hope this clarifies it for some people. Have fun, and Enjoy!