Kodak, in their wisdom, chose not to include a threaded filter attachment on the front element that telescopes out from the camera. Instead, there is a 49mm thread on the fixed "collar" that surrounds it.
One could spend ~$30 on Kodak's aluminum adapter... but I'm not that one. So it's off to the parts bin.
Step 1: Collecting Parts
Trip to the $1 parts bin at the friendly local camera store for the threaded bits: there's a wide selection of filters and stuff. The important one for the camera here is a 49mm thread part with an inside diameter big enough to let the front element extend through. The front threading should probably be 52mm or larger (to reduce vignetting, more below).
When I stopped by the hardware store I got a 1 1/2 PVC coupler - it's about the exact diameter required.
As for length... I only ended up needing 3 cm. The overall length of the barrel is shorter than the Kodak adapter to reduce vignetting - Kodak's vignettes until the camera is zoomed out according to reviews* so this isn't any worse - but this also means the camera can't zoom out to its maximum focal length. I decided to compromise between still having a very slightly wide 43mm*** available with the adapter on but not being able to go all the way out to the max 432mm, which I won't actually miss honestly.
If you want a solution that doesn't sacrifice the range, you're going to have to attach something like a step-down adapter to the front element itself. I didn't want to make a semi-permanent modification like this just yet, and I prefer this removable option for now.
** also, it reportedly interferes with close-up flash, something I avoid
*** 35mm equivalent, of course
Step 2: Rear Threading
Step 3: Front Threading
Um, be careful trying to unscrew the internal ring that holds the filter itself in the ring.
I tried giving the inner ring a tap to get the unscrewing started. It was a bit much.
On the other hand, it unscrewed really easily once all the glass was broken out.
Step 4: Attach Tube
I made a best guess as to the length (leaning toward long) and cut the coupler down. Then I reamed the inside diameter out to seat the front filter thread on.
Then just center up and glue to the rear thread. Since this rear thread has a flat face, I left the other end of the tube alone. For a regular filter ring as the rear hardware, the rear of the tube would probably need to be reamed to fit as well.
Step 5: Black Out the Interior, Install Front Threading
The interior needs to be flat black, otherwise it will reflect on the inside of the attached filter. Matte black paint marker will do, or something like black construction paper glued to the inside.
After that, center up the front hardware and glue/epoxy it on.
I used a 52mm because I already have mostly 52mm filters for my other cameras.
(Also, the original lenscap will still fit on this.)
Step 6: Outside Barrel
I had a lot of leftover "tread" material (from a treadmill) that's essentially canvas with a "rubberized" side.
I would have been smarter to see where the seam would end up when the thing was screwed on the first time I glued it on, though.