Updated after version 1.55

Gas Must Flow changed. You now need only 3 truck stops

There's a recent update that Check-In, Check-out achievement is needed only three airports instead of eight. I just got recently achievement popped out.

Some tips on getting Gas Must Flow (or some general tips for achievements which involve some rare jobs) (part 2)

3. Buy an appropriate trailer (for Gas Must Flow it's either Fuel Tank or Gas Tank). Maybe some appropriate jobs will spawn in Cargo Market. Use quick travel to teleport towards them.
4. If the job does not appear and you totally have nothing else to do, start a convoy and stop it. That'll regenerate the jobs, which gives you a chance to get a proper job. Repeat as necessary.

Tips 3 and 4 frequently appear in ATS guides comments, but I haven't seen them here. Perhaps jobs for ATS achievements are even harder to get.

Some tips on getting Gas Must Flow (or some general tips for achievements which involve some rare jobs) (part 1)

0. First discover cities and increase your level along with distributing skill points, that'll increase variety of offered jobs. Proper ADR skills are necessary.
1. Do quick jobs, that'll save you travel across the map if the job spawns far from you. Quick Travel is also an option, they happen in zero time.
2. Start working towards these achievements as early as possible, so you have something other to do while there are no appropriate jobs. Successfully Docked is a good (yet boring) filler and ferry traveling advances the game time, which will force new jobs to generate. Jobs for Driver Exceptionnel are always here (as far as you are skilled enough), so you can use special transport jobs as a filler while working towards another achievement.

The first FLE is Brent

From what i'm realising with Gas must flow, I was looking for the Éco company logo and it does not look like the one in here. It is a circle with Total on the bottom.

On "Gas Must Flow" - apparently Propane does not count either (maybe works in some other container?)

Note that "Eco" should be spelled with an accented É, which matters when sorting. It's probably worth putting in the guide that it alphabetically comes after regular E's and before F's. Also enabling the ADR filter makes it easier to search for.

Eco is also notably rare as a recipient, so it's worth putting time into getting it while working on other achievements.

Gas Must Flow!
In version 1.38, LPG works in the newer tankers.