[Kindle Fire HDX 7" & 8.9" General] ubergeek71:
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I broke out the "big guns" and attempted to repeat the dd steps on a Linux host, since it tends to be a little more forthright than Windows when something goes wrong. Connecting the device seems normal enough, as I see this in the kernel logs:

Feb 17 15:54:53 localhost kernel: usb 1-6: new high-speed USB device number 26 using ehci-pci
Feb 17 15:54:53 localhost kernel: usb 1-6: config 1 has an invalid interface number: 20 but max is 1
Feb 17 15:54:53 localhost kernel: usb 1-6: config 1 has no interface number 1
Feb 17 15:54:53 localhost kernel: usb 1-6: New USB device found, idVendor=1949, idProduct=9006
Feb 17 15:54:53 localhost kernel: usb 1-6: New USB device strings: Mfr=1, Product=2, SerialNumber=3
Feb 17 15:54:53 localhost kernel: usb 1-6: Product: QHSUSB__BULK
Feb 17 15:54:53 localhost kernel: usb 1-6: Manufacturer: Qualcomm CDMA Technologies MSM
Feb 17 15:54:53 localhost kernel: usb 1-6: SerialNumber: 1234567890ABCDEF
Feb 17 15:54:53 localhost kernel: usb-storage 1-6:1.20: USB Mass Storage device detected
Feb 17 15:54:53 localhost kernel: scsi host28: usb-storage 1-6:1.20
Feb 17 15:54:54 localhost kernel: scsi 28:0:0:0: Direct-Access Qualcomm MMC Storage 1.00 PQ: 0 ANSI: 2
Feb 17 15:54:54 localhost kernel: sd 28:0:0:0: Attached scsi generic sg1 type 0
Feb 17 15:54:54 localhost kernel: sd 28:0:0:0: [sdb] 30535680 512-byte logical blocks: (15.6 GB/14.5 GiB)
Feb 17 15:54:54 localhost kernel: sd 28:0:0:0: [sdb] Write Protect is off
Feb 17 15:54:54 localhost kernel: sd 28:0:0:0: [sdb] Write cache: enabled, read cache: enabled, doesn't support DPO or FUA
Feb 17 15:54:54 localhost kernel: sdb: sdb1 sdb2 sdb3 sdb4 sdb5 sdb6 sdb7 sdb8 sdb9 sdb10 sdb11 sdb12 sdb13 sdb14 sdb15 sdb16 sdb17 sdb18 sdb19 sdb20 sdb21 sdb22 sdb23
Feb 17 15:54:54 localhost kernel: sd 28:0:0:0: [sdb] Attached SCSI disk

According to dd, everything seems to be OK:

[root@localhost thor]# dd if=emmc_appsboot-13.3.2.3.2_user_323001720.mbn of=/dev/sdb6
678+1 records in
678+1 records out
347456 bytes (347 kB) copied, 0.704607 s, 493 kB/s

But the kernel logs suggest something is amiss:

Feb 17 15:56:18 localhost kernel: usb 1-6: USB disconnect, device number 26
Feb 17 15:56:18 localhost kernel: sd 28:0:0:0: [sdb] FAILED Result: hostbyte=DID_NO_CONNECT driverbyte=DRIVER_OK
Feb 17 15:56:18 localhost kernel: sd 28:0:0:0: [sdb] CDB: Write(10) 2a 00 00 08 00 f4 00 00 f0 00
Feb 17 15:56:18 localhost kernel: blk_update_request: I/O error, dev sdb, sector 524532
Feb 17 15:56:18 localhost kernel: buffer_io_error: 45 callbacks suppressed
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 30, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 31, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 32, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 33, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 34, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 35, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 36, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 37, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 38, lost async page write
Feb 17 15:56:18 localhost kernel: Buffer I/O error on dev sdb6, logical block 39, lost async page write
Feb 17 15:56:18 localhost kernel: sd 28:0:0:0: [sdb] FAILED Result: hostbyte=DID_NO_CONNECT driverbyte=DRIVER_OK
Feb 17 15:56:18 localhost kernel: sd 28:0:0:0: [sdb] CDB: Write(10) 2a 00 00 08 01 e4 00 00 c8 00
Feb 17 15:56:18 localhost kernel: blk_update_request: I/O error, dev sdb, sector 524772
Feb 17 15:56:18 localhost kernel: sd 28:0:0:0: [sdb] Synchronizing SCSI cache
Feb 17 15:56:18 localhost kernel: sd 28:0:0:0: [sdb] Synchronize Cache(10) failed: Result: hostbyte=DID_NO_CONNECT driverbyte=DRIVER_OK
Feb 17 15:56:18 localhost systemd-udevd: inotify_add_watch(7, /dev/sdb6, 10) failed: No such file or directory

which certainly makes it appear that the write is failing. I've tried a couple of different USB cables (even though the original one was working fine with adb and fastboot).