Ani lo nogea be'kesef¹ samim meluchlach.
¹ from Glinnert's Modern Hebrew: Essential Grammar: "The Hebrew of broadcasters, teachers and their ilk make certain complicated adjustments in pronouncing words beginning with a prefixed וְ , בַּ , כַּ , לַ. Colloquial Hebrew generally doesn't bother." (I think this is begedkephat, but maybe someone can explain/confirm/deny why he prounced kaf as chaf).
In short and as I recall learning from Randall Buth's notes in his Living Biblical Hebrew curriculum, the בְּ (written with a shva na' under it) preceding the כ is pronounced more-or-less with a (half-)vowel. Because the כ is a begedkefet consonant (just you already observed), it is pronounced as a fricative rather than a stop.
If you respond to this reply, I can try to dig up a relevant quote with just a little more info later.