Yes Burns is a Johnson stooge. He was the one whispering to Johnson right before Johnson made his claim about Starmer protecting Savile.
He doesn't have the nicest track record himself -
"The international trade minister, Conor Burns, was found by the standards committee to have made a series of veiled threats while attempting to intervene in his father’s dispute over a loan.
The committee recommended a suspension from parliament over multiple breaches of the MPs’ code before No 10 announced his resignation. A Downing Street spokesman said Burns had resigned after the committee’s report."
amp.theguardian.com/politics/2020/may/04/uk-trade-minister-conor-burns-resigns-over-loan-threats