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The front fender looks correct, the rear has a re-pop that someone has unfortunately cut it to fit.
NBHAA is correct. After AMF bought CWC they began adding a separate year mark to the right of the serial number. At first they used "52Cw" (for 1952) and kept that system until sometime during 1956, when they changed over to "F" (they bought CWC in 1951 and if you take 1951 as "A", then 1956 is "F"). In 1958 they changed again and started using the year letter (H for 1958) at the beginning of the serial number. The early AMF serials look similar to the CWC serials, but it's a different system. And the system changed again in the early '60's when they started using more than one letter per year. My only concern is that the 1956 AMF catalog still lists the Luxury Liner as having balloon tires (26 x 2.125) and this bike looks like a middleweight. The Luxury Liner was the last balloon tire AMF and became a middleweight for 1957, so I'm guessing that this number was stamped late in the year and the bike was actually built for 1957. I have a middleweight Flying Falcon stamped "54Cw" under the bottom bracket, but the first mention of the middleweight F.F. is in the annual catalog, printed March 1955. The re-pop Luxury Liners were ballooners and I can see how someone would have to cut the fender to fit.
That’s a lot of great information, I literally knew nothing about this bike that week ago. Just picked it up on a whim. So far it’s been the most challenging of all the bikes own. Really curious about the multiple speed powered brake. I don’t think I’ve seen a model online that has one. Just this ad.
The "multi-speed power brake" is a Bendix two speed with a coaster brake. Pretty common in the late '50s.
From the catalogs I've seen, AMF only offered the two-speed on the L.L. in 1956, but they were standard on the middleweight F.F. for 1955 and '56, and they've also turned up on bikes AMF badged for other retailers, like Hiawatha and American Flyer. If you're not sure whether your bike was built as a ballooner or a middleweight, check the rear fender bracket. The top picture below is for balloon fenders, the bottom shows the middleweight bracket. I need to get a better picture of the balloon fender bracket, it's not quite in focus.
If you've got the balloon bracket then I wonder why the re-pop fender had to be cut? The re-pops were for the earlier style but I think the later style like yours was introduced in '54, about the time they adopted the rear drop-outs instead of the rear fork, so there may have been other changes to the frame. It would be interesting to get two examples side by side to compare. Nice bike!
Come to think of it, the bikes with rear forks always had a dip in the chain stays just in front of the axle to give access to the adjusting screws and your bike doesn't have that, so there had to be a change in the geometry.
