I've got some more information on Killstreak kits.
They come in three varieties: standard, specialized, and professional.
Standard: You're guaranteed to get one for a random weapon upon completion of a Two Cities tour. Applying one to a weapon adds a UI feature next to your health meter (for those using the standard UI) which keeps track of your current life's killstreak. In addition, any time you kill with that weapon, your killfeed notice will also display a number alongside your kill icon corresponding to your killstreak. Every 5 kills a notice will flash under the timer to everyone (I think) claiming you have made x*5 kills in a typical Quake fasion (Kill streak! Unstoppable! God-Like). After 25 kills, you will be "Still God-Like" every 5 kills after. The MvP screen at the end of the round will also show who on the winning team (or either in the event of a Stalemate) had the highest streak of the round if someone is using a Killstreak-equipped weapon.
Specialized: From what I can tell, you're guaranteed a fabrication kit for one of these after completing a Two Cities tour. You can also get one as a random prize for completing a mission in Two Cities. In addition to the Standard Killstreak functionality, Specialized Killstreak kits add a visible color sheen to your weapon. The sheen causes your weapon to glow a specific color periodically, based on what the kit says. The higher your killstreak, the more frequently your weapon will glow, with 10+ kills having the highest glow rate.
Professional: These are a rare drop from completing a Two Cities tour, more rare than Specialized kits, but less rare than Australium weapons. In addition to the visible sheen and the killstreak functionality, you'll also have a particle effect emitting from your class' eyes after 5 kills based on what it said on the bottle. This effect is the same color as the weapon sheen and becomes more intense after 10 kills.
Standard kits can be used straight out of the box if you get one. Specialized and Professional fabricators are required to make the higher tier killstreak kits however. These work like Chemistry Sets; fulfill the requirements of the fabricator and the prize is yours. The fabricators ask for a random assortment of parts you get for completing Two Cities missions (and possibly other MvM missions, have not tested this). It will ask for something along the lines of 28 or 29 parts along with a matching killstreak weapon or two for the output. Specialized Kits require 5 uncommon parts (Reinforced) and 24 common parts (Battle-Worn) along with a standard Killstreak weapon matching the kit's output (so if you have a Bonesaw fabricator, you need a Killstreak Bonesaw). Professional fabricators require 16 common parts, 6 uncommon parts and 3 rare (Pristine) parts, along with 2 Speclialized Killstreak weapons matching the output. With the market in it's current state, this can run a lot of money; I had to get $30 worth of Flamethrowers for my Professional kit. Weapon inputs must be Unique quality (yellow).
A finished Killstreak Kit can be applied to any weapon regardless of quality. As such you can have Vintage, Strange, (Strange) Festive, Genuine, Collector's, or Haunted Killstreak weaponry. From what I can tell, every weapon except a few specific promotional weapons have a corresponding kit. So far, the weapons I know that don't have kits: Lugermorph, Big Kill, Frying Pan, Black Rose, Headtaker, Golden Wrench, Saxxy, Memory Maker.
I've got a Professional Kit on my Flamethrower with the Tornado effect and Purple Sheen, here's what it looks like: