Having done a straw poll at work all agreed that the example given was very ambiguous and that the pilot was right to question it. The solution would be either to start the transmission with "ABC Climb FL350, from KOK track direct BOMBI", or break it up into two separate transmissions, or reitterate the whole clearance, ie. "ABC cleared present position KOK direct BOMBI, Climb FL350." As there is no mention of "after" there is no confusion as to when to climb.
Certainly in agreeance that saying ABC after KOK track direct BOMBI climb FL350, does leave it open to interpretation as to whether you mean climb now, or after KOK. Poor phraseology, very poor.