But if he says 'bishkuna' then the kaf should be hard (kaf) not soft (chaf). He seems to be breaking the bgdkft rules here.
If it breaks your rules, you do not have enough rules ;-) After a vowel must always follow the soft form of the begadkefat letter, but after a consonant, usually the hard form is used, but not always, like in מַלְכֵי־ (kings of) or שַׁרְבִיט (scepter). When you combine the monoconsonantal prepositions with a noun, the onset second syllable does not change to its hard form: בְּ+דְּבָרִימ becomes בִּדְבָרִימ [bidvarim]. This phenomenon is called Sheva Medium or שווא מרחף (look it up on page 11).