What does the Poynting flux represent?
Energy flow associated with wave motion. See this Blaze Labs picture:
The Poynting vector is pointing in the direction the wave is travelling, transporting E=hf energy. Or energy-momentum if you prefer.
I know that the Poynting flux is the cross product between $\vec E$ and $\vec B$
I'm afraid there aren't really any such fields, see Jackson section 11.10 where he says "one should properly speak of the electromagnetic field Fμν rather than E or B separately". Also see the Wikipedia electromagnetic radiation article and note this: "the curl operator on one side of these equations results in first-order spatial derivatives of the wave solution, while the time-derivative on the other side of the equations, which gives the other field, is first order in time”. If it was an ocean wave and you were in a canoe, E denotes the slope of your canoe and B denotes the rate of change of slope. There's aren't two waves present, just one, and it's an electromagnetic wave, which is an electromangetic field variation.
but I'm wondering, are the field lines of the Poynting flux considered as electromagnetic energy?
I'm not sure field lines is quite the right phrase, but I'd say the answer is yes. Think about pair production and electron spin and spin angular momentum, then take a look at the static fields section of the Wikipedia Poynting vector article. The Poynting vector is still orthogonal to both E and H, only now it it isn't linear, it goes round and round:
Public domain image by Michael Lenz, see Wikipedia
"Although there are only static electric and magnetic fields, the calculation of the Poynting vector produces a clockwise circular flow of electromagnetic energy, with no beginning or end. While the circulating energy flow may seem nonsensical or paradoxical, it is necessary to maintain conservation of momentum. Momentum density is proportional to energy flow density, so the circulating flow of energy contains an angular momentum".
This angular momentum is exhibited via the Einstein-de Haas effect which "demonstrates that spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics.".
Let's say we have charged particles in this field, would the Poynting flux exert force on them and move them along the field lines?
Yes. If you had two charged particles such as an electron and a positron (see the Wikipedia positronium article), they would move linearly and/or rotationally, something like this:
But note that this is a simplified "flat" picture. The positron has the opposite chirality to the electron. Both are Dirac spinors, and a Dirac spinor is a bispinors. It's like you've have a steering-wheel rotation, and a coin-spin rotation both going on at the same time, one at twice the rate of the other, hence spin half.
I have a plot of a Poynting flux that looks like this:
What would happen if there were charged particles in this field?
This field looks like it is the field of a charged particle such as a positron. If you placed an electron down near it, linear motion would happen. Counter-rotating vortices attract, co-rotating vortices repel. If you threw the electron past it, rotational motion would also occur.
All this might sound novel, but don't forget Maxwell's page title. Or that in atomic orbital electrons exist as standing waves. Standing wave, standing field. And when you have a standing wave in a mirror-box, when you drop one of the sides that wave is off like a shot from a standing start, because there always was motion at c, even though you couldn't see it. It's the same for electron-positron annihilation.