I highly doubt the BF CLP itself was the issue! More than likely you had years of crud built up in the cylinder and the BF CLP just temporarily softened it up and then the crud congealed & clogged it. You need to fully disassemble the cylinder, clean it with Hoppes #9 solvent, dry and lightly lubricate it. BTW, all CLP's must be shaken before use. BF is an excellent CLP. That said, I personally like G96 Synthetic (yellow bottle) better. IMHO the G96 just works a bit better than the BF as I have discovered lately. Especially in the cleaning aspect. Both lubricate and protect well.
While I am usually not a fan of spraying chemical into an assembled unit, if you really do not want to or do not feel comfortable disassembling the cylinder, use some Gun Scrubber to clean out the inside until it drips clean. Thoroughly dry it out with compressed air and then lightly lubricate it. That should do the trick.