The Labour leader also demanded other ministers come clean over their own tax arrangements after Sajid Javid admitted holding non-dom status before he became an MP.
His comments came on a day Downing Street insisted the Prime Minister retains full confidence in Mr Sunak.
Speaking to reporters in Sunderland, Sir Keir said: “While he insists on making working people pay more taxes, the Prime Minister owes it to the public to confirm his Cabinet are not finding ways to pay less.
“The scale of the Chancellor’s hypocrisy is difficult to swallow against the backdrop of a cost-of-living crisis. We now know that the Health Secretary – the former chancellor – also knows his way around a tax-reduction scheme.
“To appoint one chancellor with suspect tax affairs is sloppy, to appoint two is a habit. It really is one rule for them, and another for everyone else.
“For every day this chaos continues, energy bills are going up, prices are going up, and this Government isn’t doing anything to help people paralysed by the cost of living crisis.
“Boris Johnson needs to bring this saga to a close and confirm that no other sitting Conservative minister is doing or has done anything to reduce their own personal tax bill, while they preside over the biggest tax hike in 70 years.”
The former head of the CPS also claimed there were "all sorts of issues" in relation to the ministerial code, and questioned the tax arrangements of others in Government.
He said: “That’s why it’s so important I think for the Prime Minister to give that assurance: have other members of your Cabinet Prime Minister been making use of schemes to reduce their own taxation?
“The Chancellor should just put those answers into the public domain so everybody can see the answers to the very obvious questions that are being asked and we have transparency and accountability.
“What we can’t have is a Chancellor who is telling millions of people that they have to pay more tax, there is no alternative, whilst at the same his own family appear to have been using a scheme to keep their own tax down.”
Earlier the Prime Minister agreed to a request from the Chancellor to launch an investigation into the Chancellor’s ministerial interests.
Asked if Mr Johnson continues to have full confidence in the Chancellor, a No 10 spokeswoman said: “He does.”
She also confirmed Mr Johnson had accepted Mr Sunak’s request for an investigation by Lord Geidt, the Prime Minister’s independent adviser on ministerial interests.
Asked if Lord Geidt had begun his investigation into the Chancellor, the spokeswoman said: “I’m not aware of whether Lord Geidt himself has begun his work.
“But I can confirm that the Prime Minister has agreed to the request from the Chancellor for Lord Geidt to undertake this work.”
In a letter to the Prime Minister, Mr Sunak asked for Lord Geidt to review all his declarations of interest since he became a minister in 2018 to ensure they had been properly stated.
He said he was confident he had acted appropriately at all times, but his “overriding concern” was that the public should have confidence in the answers.