Hi, You recommend against using pillows but what about the pillows that are designed to correct and prevent the flat head syndrome? Are those pillows not recommended either? If not for sleeping how about for other times when on their back?

You are correct that Red Nose does not recommend the use of pillows due to the risk of suffocation & overheating.
Pillows are not necessary for baby while baby is sleeping unobserved.
Red Nose is aware of research showing that the use of a pillow in baby’s sleep environment increases the risk of Sudden Unexpected Death in Infancy (SUDI), including Sudden Infant Death Syndrome (SIDS) and fatal sleep accidents.
They may cover the baby’s face and obstruct breathing or cause overheating.
Older babies in a cot can be at an increased risk of a sleeping accident by using pillows as a step to climb up and fall out of the cot.
Some physiotherapists and chiropractors have recommended the use of a pillow to relieve the flattening a baby’s head, a relatively common condition, known as positional plagiocephaly.
This is not suitable while baby sleeps unobserved.
https://rednose.org.au/article/pillow-use
https://rednose.org.au/article/can-baby-use-a-pillow-to-prevent-flat-head

There are many ways, including tummy time when awake, to reduce the incidence of flat head in babies.
it is important to limit the amount of time baby is on back when awake.
https://rednose.org.au/article/babys-head-shape