Well, I've flown across the Atlantic from Finland to Florida to get tattooed and it was honestly fine. I've also been traveling to London every year for the past 3 to get my legs worked on and its been easy. Just book an appointment, book flights, get time off from whatever and go! Its no different from any other trip and tattoos are the best thing to bring back...
I booked a full day each time which ended up being somewhere between 7-10hours each time. I've also both flown out the next day after the session and taken a day of rest before flying and there was no difference or trouble doing either at all. And both Delphine and Laurent have been real cool about this arrangement the whole time, I actually think its a bit weird for an artist to be difficult with someone for having time between sessions if you're traveling to see them and have a decent session even if its years apart. But then again more and more artists seem to act like complete divas these days... I choose to go to tattooers who are good people in addition to being good artists. Makes for better memories AND tattoos.
and I guess I'll mention that the first time I had both knees worked on by different artists at the same time, and yes they were sore but flying back the next day was still fine, and I'm a tall guy.