Can I use slider dropouts on my track dropouts?
If your rear spacing measures 115mm it might actually be designed as 110mm or 120mm. See here for standard hub spacings. 

120mm freewheel hubs should be available, but you will only be able to fit a 5 speed freewheel onto it. If the frame is 100mm and steel you can probably expand the spacing to 120mm - see the page linked above for how that is done.

You will not be able to buy a 120mm hub with a disc rotor attachment. Disc rotors take up space, so hubs and frames had to get wider to accommodate them and keep the spoke flanges separated enough to maintain wheel strength.

Personally, I wouldn't trust a disc brake conversion kit period, especially one that relies on a couple of tabs in the slot dropout to resist braking torque like the one you included a picture of. A decent set of rim brakes should be plenty powerful enough.

Also, the kit pictured moves the rear wheel attachment out of the actual frame dropouts. Again, I wouldn't trust that particular kit. There are slot dropout derailleur hangers available that keep the axle bolted in the frame.