Yoga flow, or flow yoga, has become very popular over the past 10 years & more. But what exactly is it? In modern understanding, it's a flowing style of yoga, called vinyasa yoga, whereby one posture is connected to another, with emphasis on types of surya namaskara (sun salutes), in particular the surya namaskaras A & B, from the Ashtanga Yoga of Pattobhi Jois. So, these 2 surya namaskaras have been modified in many cases, with warrior poses, trikonasanas (triangle poses), planks, standing balances, arm balances, jumping forwards & backwards.....a whole moving scenario of hard poses, finishing often with bridge pose & cooling down leg, buttock, & twist, stretches. Sometimes abdominal work &/or back work is added.
When it's all done very vigorously, it's usually called hot yoga, because it is incredibly heating. And hard. Very athletic. When the yoga session is done a bit slower, it's more flow yoga, & when ujjayi pranayama is also used with the slower style, it becomes more meditative.
Frequently, the asana precision of Iyengar yoga is added, & the adjusting of the session to suit individual abilities, this brings in the teaching attitude of Desikachara. Jois, Iyengar, & Desikachara, were the three most famous names from the teachings of Krishnamacharya, a great yogi & teacher.
There is another style of yoga flow, from Kali Ray, the founder of Triyoga. She called her flow Prasara: flowing without thought, because all the yoga that she teaches, has flowed through her. It just manifested, Kali says, & includes over 1000 hasta mudras (hand gestures) as well as pranayama & meditation. It is a very systematic, meditative, slow moving form of yoga, & she calls many of her poses "flows". Many do actually flow between 2 poses, eg reverse plank to seated forward bend (paschimottanasana). Some are longer sequences that "flowed" out of her. Kali says that she 1st introduced yoga flow in a big way, at at a yoga conference, over 20 years ago.
For me, this is more of an authentic form of yoga flow. The yoga flows through, out of, a person. For most of us, this comes after much training in a system, which leads to a type of "unconscious" knowing of what, when, how, why, to teach yoga. It becomes part of one, whether one is teaching beginners or advanced, physical or spiritual. The knowledge, it too does just flow from a person, from their own accumulated years of practice, & knowing, instinctively, what will be best for a person. Posture sequences may manifest as one practices, or hand mudras, pranayama sequences, dharana (concentration) techniques. This is all quite different from someone who will try & make sequences from poses that they have learnt. Or, someone who reads then teaches what they have read. Quite different.
Yoga is most definitely both a scientific & a spiritual system. Even if we start with a scientific outlook, the spirituality within will want to flow out of us. Our spirit comes alive & we start to want to live yoga, to do, to our best ability, our best with truth, kindness, our spirit starts to show, & the yoga starts to flow, as a way of life, from within.