Qualify for 144 hour pass?

Correct. You need either a visa or different flights.

Even for a 3 hour layover from Beijing to Thailand disqualify me from the 144 hour pass in Beijing?

Yes. Even a 1 minute stop, even if you don’t get off the plane. You’re not qualified for 144 hours transit without visa.

Most trips going from LAX has a stop over in Shanghai for 3 or 4 hours. Then Shanghia to Beijing where I want to use the 144 hour pass. But my ultimate destiny is Bangkok has a 2 hour layover in Kunming, China. That will disqualify me for the pass? Most trips from Beijing to Bangkok has layovers. I couldn't find one flight, stopping at Beijing for 144 hours, then flight to Bangkok without a stopover.

Then you need a visa. It is always the passenger's responsibility to comply with immigration regulations in another country.

There are multiple non-stop flights every day from PEK to BKK. You could also transit in HKG, etc. Your Bangkok flight doesn’t need to be on the same ticket; two separate tickets will be fine.

If you’re trying to do a package deal such as on Priceline multiple destinations you will end up stopovers to Beijing such as Shanghai and another stopover to Thailand from Beijing such as Kunming. Buying separate flights will be much higher.

Then either get a visa or get a better travel agent.