The phrase "are continually becoming" is correct and usable in written English.
It can be used to describe an ongoing process of change or transformation over time.
Example: "As society evolves, we are continually becoming more aware of the importance of sustainability."
Alternatives: "are constantly evolving" or "are always transforming".
New processes are continually becoming available to the chemical engineer to accomplish these ends.
Since Chandra is an on-going mission, new observations are continually becoming public.
Once past the crisis, we must absorb all of the learning, so that we are continually becoming better at preparing and responding.
Everything from parking meters and garbage cans to mail boxes in our cities are continually becoming smarter, increasingly connected and more efficient as parts of a larger city networks.
Except when it's been specifically processed to counteract this (and can we really call those slices "cheese," anyway?), cheese is continually becoming cheesier.
Eventually, the shape of my body will actually change, not superficially, but structurally, internally, and that new shape will in turn inform who I am continually becoming.
It is continually becoming cheaper, faster and more reliable, with the capability to identify rare yet clinically important somatic mutations.
It is essential to have clear, detailed rules on the subject especially as the technology available for users is continually becoming more sophisticated".
Water quality standards are continually evolving, usually becoming more stringent.
Prevention of host cell detachment and limiting cell turnover is an important strategy of bacterial pathogens as host intestinal enterocytes are continually being replaced, preventing many harmful invaders from becoming established.
However, health care workers (HCW) are continually exposed to the bacilli at endemic sites presenting increased chance of becoming sick.
