Per wikipedia the Concorde and 707 are vaguely similar size and the Concorde successfully pulled off 15 passenger miles/gallon and the 707 got about 30 passenger miles/gallon around the same time.

Now JetA isn't service station gas so its slightly unfair to compare the 15 pMPG of a Concorde to a 12 MPG single passenger pickup truck. But it does give you a general idea that everything being equal (size, technology level, risk?) the supersonic plane will burn about twice the carbon footprint of a similar subsonic plane.

Note that with a full modern subsonic plane its quite easy to get a carbon footprint staggeringly better than a single driver in an obese modern SUV or truck. The problem is if you're fair and let the aircraft people use any thing they want such as 2016 technology and engineering, you have to let the car people use any thing they want, and my wife's Prius is trivially capable of providing reasonable comfort at 300 passenger miles per gallon.

Supposedly the largest 777 model does better than 70 pMPG per my commercial pilot buddy (who teased me quite a bit about my wife's Prius only getting 60 pMPG when there's only one passenger, so he burns less gas flying than she does driving). So everything being equal if stereotypical subsonic planes have roughly doubled in pMPG then its not ridiculous to expect over 30 pMPG on a modern supersonic plane. My Yaris commuter car struggles to get 30 pMPG with a single passenger (me) so to a first approximation a modern supersonic aircraft damages the environment about as much as driving alone in my subcompact commuter car. Not great, not awful. Eh.

Obviously my car's performance in transatlantic and transpacific service is somewhat inferior to the performance of the proposed plane.

The other big factor to keep in mind is Concorde hourly fuel consumption at cruising subsonic speed (something below Mach 0.95) was pretty much disastrous as it was the same than at vmo (which was Mach 2.02).

So the goal was always to go supersonic as quickly as possible as the fastest she went the better the mpg got...

mpg isn't really relevant, though. If you fly a few international flights a year, or even coast to coast, you can easily rack up many more miles than you would drive. Flying easily dwarfs the carbon footprint of driving.

Well, technically Prius would have 300-ish pMPG. If a pilot was the only person in the plane, it's pMPG would be much much worse. Even better comparison would be a shuttle bus pMPG..

But that depends on how it's typically operated. Nobody uses an airliner as a one-person transport, but unfortunately many people use a Prius that way.

On average, airplanes are not used to 100% capacity either. Some flights are oversold, some are half-empty. Sometimes they're almost empty. Cars frequently are occupied by 2 or more people, sometimes they are full too.

I never saw any hard statistics, but it's definitely not cars 90% 1 occupant, planes always near-full. It's anecdotal evidence for sure, but my car is, on average, as full as average plane I took. Especially if we count per-mile rather than per-trip.

Things also get weird with air cargo. My pilot buddy says they fill the cargo area and aircraft to the weight or volume limit pretty much every flight he takes. He may fly for a weird carrier or on weird routes, but it sounds believable that there is infinite supply of "I wanna get there faster" cargo. You might see ten empty seats but merely means there's a one ton MRI thingie that's on emergency shipment in the cargo area. He mentioned they're really into containerization and a small container alone costs $200 so I am almost scared to ask how much it costs to actually ship it. Then again everything aerospace rated costs a hundred times more, so a $2 isn't so ridiculous.

Aacargo.com division of american airlines proudly advertises they ship 100 million pounds of cargo per week, and also advertise they have 6000 flights per day so thats averaging about a ton of cargo on every flight and a ton represents maybe ten empty passenger seats, so your average flight should have ten empty seats. Of course reality is the seats might be near empty at midnight and 100% full during the day, etc.

Both kinetic energy and air friction scale approximately with N^2. (Where N is units of velocity.) One can escape a lot of air friction by going higher, which is what Boom is planning to do, but you have to pay for the potential energy of altitude with fuel. Boom is minimizing the weight by using carbon fiber. (Which also means the wings have to redirect less air to keep the plane in the air, which also reduces drag.)

It's likely that the carbon footprint is several times higher, perhaps nearing an order of magnitude.

That would depend heavily on the effect on the volume of flights, fuel per seat per mile, the energy inputs to constructing the plane & its maintenance parts, and their sources...