Musk flies in a Gulfstream G650 ER private jet, a top of the line airplane. It has a cruising speed of 890 km/hr. I'll assume this speed for all of his flying time, though of course it's lower during takeoffs and landings, or "short" trips at lower altitudes, etc. We're just doing an estimate here, a lower limit.
So Musk spent at least 271 hours flying privately last year. That's 11 days, or 3.1% of the year.
Musk may have flown with family and friends, but since the trip was being taken at his behest, he alone owns all the fuel burned and carbon emitted.
I couldn't find fuel data for the Gulfstream G650 ER, but did find this for the Gulfstream 400: fuel consumption of 32 liters/minute. Let's use that.
Note added: See below.
So Musk burned about 520,000 liters of jet fuel last year. That's 138,000 gallons, or 21% of the volume of an Olympic-sized swimming pool.
Jet fuel emits 9.57 kg CO2/gallon. I don't know about fuel for private jets, but let's use this figure for the estimate. I'll assume jet fuel has the same density as water.
So Musk's flying footprint for 2018 was 1.4 M kg CO2, or 1.3 kt (kilotonnes).
US per capita CO2 emissions are about 17 t CO2/yr, so Musk's total is equivalent to about 77 Americans.
But World per capita CO2 emissions are about 5 t CO2/yr, so Musk's emissions were equivalent to 263 average world citizens.
Note added 12:40 pm: I found an important number and can improve on this estimate some: the Gulfstream 650 burns 1,100 kg of jet fuel per hour. This brings Musk's flying carbon emissions for 2018 down to 750 tonnes of CO2, or 0.75 kilotonnes, which is like 44 average Americans or 150 average global citizens.