The prewar numbering system for the Flyer 3/16ths O gauge trains is screwy - the 4-8-4 Challenger was available in standard worm gear drive models, worm gear drive with RDC models (the reverse unit controlled by a relay that was triggered by DC ala the way Lionel triggered the whistle in their whistle tenders - the Flyer engine would continue running in the same direction, even if power was cut and then restored until the jolt of DC triggered the reverse unit to cycle), spur gear models with RDC, kit version models - the catalog/dealer ordering numbers didn't always match the number stamped on the cab. Luckily, the valve gear/linkage/siderods are the same for all the prewar O gauge variations of the 4-8-4 Challenger.
The parts number for the side rods for a prewar 3/16ths O gauge 4-8-4 is the same as the part number used for a postwar S gauge 332/335/336 4-8-4; the part number is PA8994-A, and you should be able to easily obtain those. The parts that were used to assemble the valve gear/linkage have common parts except for the 3/16ths O gauge version having a dogleg bend on one piece that clears the wider axle spacing of the drivers for 3 rail O gauge track. I've never seen a parts listing from parts dealers that listed the 3/16ths O gauge valve gear/linkage assemblies - you'll in all probability need a carcass to harvest the valve gear assemblies (ebay is where I used to score junkers when I had a layout and ran Flyer 3/16ths O locomotives - those were moved on to other folks when my layout came down about 15 years ago).
Years ago I obtained a large lot of factory paperwork from AMT and A.C. Gilbert that was addressed to Fort Wayne, IN model train dealer Ralph Calvert. The Gilbert paperwork contained notes requesting 3/16ths O gauge parts, and more importantly a parts listing dated June 20, 1947 for the 3/16ths O gauge line. I shared this information with my friend Art Shifrin, who was waist deep into collecting/restoring/running prewar 3/16ths O gauge Flyer. Art kindly took scans I made of the paperwork and cleaned/sharpened the images in Photoshop - I compared the O gauge part numbers on the factory parts list with the factory parts diagrams for the postwar S gauge 4-8-4 locomotives in the K-Line Complete Service Manual for American Flyer Trains and found the side rod part numbers matched.