Mother-of-nine Katherine Cox, 33, and boyfriend Danny Shepherd, 25, deny causing or allowing Eli Cox's death.
Sam Holmes told Maidstone Crown Court that when he arrived at their Minster home "lots of adults were running around not knowing what to do".
The jury also heard how the couple had delayed the departure of the ambulance.
Mr Holmes said he had to repeatedly ask them to get into the ambulance with the baby.
"It took a while. They were running around asking for keys. I had to repeat it three times," he added.
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Paramedic David Goodale told the jury that he also had to "ask several times for the family to get into the ambulance".
When asked by prosecutor Jennifer Knight what else he remembered of that day, he said that Ms Cox was on her phone "throughout the journey" to the hospital.
"I feel when we were asking her questions about the background of Eli she wasn't quite giving them. Danny gave us his history."
Mr Goodale said he was told by Mr Shepherd that "Eli had been unwell, he had vomited, he vomited again and went blue".
"He said he tried to blow into his mouth," he told the jury.
When asked if he remembered "seeing or smelling vomit on Eli's clothes", Mr Goodale replied: "No. There were no signs of vomit."
The court heard that paramedics spotted small red marks on the baby's cheeks, which Mr Shepherd told them were caused by Eli scratching himself with his finger nails.
Ms Cox's son Eli died in hospital on 27 April 2016, two weeks after the incident in Kent.
A neighbour of the couple, Mary Anne Davies, who is also trained in first aid, told the court that she had to "chase" Ms Cox into the ambulance.
"Any mother would have gone, just gone," she recalled.
She added that she also remembered hearing Mr Shepherd say: "Watch me get the blame for this."
Post-mortem examinations showed Eli's death was caused by a head injury of a "shaking or shaking impact type".
He also had oxygen deprivation to his brain, a brain injury, bruises at the back of his head and fractures dating back weeks before his death.
The court heard a hair sample showed he had been "regularly exposed to amphetamine and occasionally exposed to cocaine".
The trial continues.
An ambulance technician has told the trial of a couple accused of causing the death of a five-month-old boy how he was met with "complete panic".