If behaviourism is focused upon observable behavioural dispositions can it at all account for qualia; the way things feel, tase etc.
It seems answer is no.
In fact, qualia is one of argument against Behaviourism.
For example, some zoombie can behaves exactly as Praying to God and chanting God's name but without any 'feelings' of devotion or praying which normally one experience in himself (who is not philosophical zoombies). Or if someone read Bible or Bhagavad Gita, then there is "something extra" to meaning and learning than mere behaviours associated with our body expression or behaviour while speaking or learning.
A second reason for rejecting behaviorism is that some features of mentality—some elements, in particular, of the conscious mental life of persons—have characteristic ‘qualia’ or presentationally immediate or phenomenal qualities. To be in pain, for example, is not merely to produce appropriate pain behavior under the right environmental circumstances, but it is to experience a ‘like-thisness’ to the pain (as something dull or sharp, perhaps). A purely behaviorist creature, a ‘zombie’, as it were, may engage in pain behavior, including beneath the skin pain responses, yet completely lack whatever is qualitatively distinctive of and proper to pain (its painfulness).
Also Behaviourism can't satisfactory explain about behaviour related to language in children:
In a review of Skinner’s book on verbal behavior, Chomsky (1959) charged that behaviorist models of language learning cannot explain various facts about language acquisition, such as the rapid acquisition of language by young children, which is sometimes referred to as the phenomenon of “lexical explosion.” A child’s linguistic abilities appear to be radically underdetermined by the evidence of verbal behavior offered to the child in the short period in which he or she expresses those abilities. By the age of four or five (normal) children have an almost limitless capacity to understand and produce sentences which they have never heard before. Chomsky also argued that it seems plainly untrue that language learning depends on the application of detailed reinforcement. A child does not, as an English speaker in the presence of a house, utter “house” repeatedly in the presence of reinforcing elders.
Behaviorism can account for qualia as well as, if not better than, other schools of psychology. The premise of the question has to be reframed, though. Behaviorism is not focused only on behavioral dispositions—that describes methodological behaviorism which is roughly a century out of date. BF Skinner, who advocated radical behaviorism, was quite clear about not excluding events “within the skin.” As he said in About Behaviorism (1974)
Radical behaviorism…does not insist upon truth by agreement and can therefore consider events taking place within the skin. It does not call these events unobservable, and it does not dismiss them as subjective. It simply questions the nature of the object observed and the reliability of the observations.
The position can be stated as follows: What is felt or introspectively observed is not some nonphysical world of consciousness, mind, or mental life but the observer’s own body.
What is inside the skin, and how do we know about it? The answer is, I believe, the heart of radical behaviorism.
So a behaviorist, for example, might detect that a dog cannot discriminate between red and green, no matter how the dog is reinforced, in much the same way that a colorblind person can’t see certain numbers on an Ishihara test. Behaviorist psychologists following Skinner would have no problem saying the dogs or some colorblind individuals “can’t see red.” In fact, most of what we know experimentally about how people experience the world in terms of qualia are from these types of tests where subjects have to discriminate between one stimulus and another—these tests fit squarely within behaviorism.