Após reiniciar o kernel genérico do Slackware, notei que o SDcard foi detectado como um dispositivo SCSI - a saída do dmesg segue:
[ 205.694553] usb 2-2: new high-speed USB device number 3 using ehci_hcd
[ 205.812086] usb 2-2: New USB device found, idVendor=0cf2, idProduct=6250
[ 205.812100] usb 2-2: New USB device strings: Mfr=1, Product=2, SerialNumber=4
[ 205.812109] usb 2-2: Product: UB6250
[ 205.812116] usb 2-2: Manufacturer: ENE Flash
[ 205.812122] usb 2-2: SerialNumber: 606569746801
[ 205.841074] scsi3 : usb-storage 2-2:1.0
[ 205.842222] usbcore: registered new interface driver ums_eneub6250
[ 205.848453] keucr: module is from the staging directory, the quality is unknown, you have been warned.
[ 205.850027] usb --- usb_stor_init start
[ 205.850103] usbcore: registered new interface driver eucr
[ 205.850109] ENE USB Mass Storage support registered.
[ 207.175693] scsi scan: INQUIRY result too short (5), using 36
[ 207.175714] scsi 3:0:0:0: Direct-Access PQ: 0 ANSI: 0
[ 207.177069] sd 3:0:0:0: [sdb] 3911680 512-byte logical blocks: (2.00 GB/1.86 GiB)
[ 207.177250] sd 3:0:0:0: [sdb] Write Protect is off
[ 207.177262] sd 3:0:0:0: [sdb] Mode Sense: 0b 00 00 08
[ 207.177437] sd 3:0:0:0: [sdb] No Caching mode page present
[ 207.177445] sd 3:0:0:0: [sdb] Assuming drive cache: write through
[ 207.179216] sd 3:0:0:0: [sdb] No Caching mode page present
[ 207.179230] sd 3:0:0:0: [sdb] Assuming drive cache: write through
[ 207.208861] sdb: sdb1 sdb2 sdb3
[ 207.209959] sd 3:0:0:0: [sdb] No Caching mode page present
[ 207.209971] sd 3:0:0:0: [sdb] Assuming drive cache: write through
[ 207.209980] sd 3:0:0:0: [sdb] Attached SCSI disk
A linha ENE USB Mass Storage support registered
insinuou que havia algo faltando relacionado ao suporte a USB, então encontrei essa opção que estava desativada: Device Drivers->USB Support->USB ENE card reader support
. Depois de recompilar o kernel incluindo este módulo, foi possível acessar o SDcard como de costume através do dispositivo de bloco SCSI associado.