Considering that the Emperor seemed to need the power of the Chaos Gods to build the basis of the imperium. (I think there are some references about this in the book, ‘The sigilite’) Is there any reference in the Warhammer40k RPG books regarding the initial relationship between the Emperor and the 3 former Gods of Chaos (namely Khorne, Nurgle and Tzeench)?
They have never been on "Good" Terms
Chaos and the Emperor have always been at-odds, however, what the exact story is tends to vary.
The most generally-accepted origin story, and by that I mean the one most-often referenced by the community and by GW itself, is the story of the Shamans, sourced from Realm of Chaos: Lost and the Damned (1990).
Realm of Chaos: The Lost and the Damned
In this version, the Emperor is the combination of the souls of a group of human Mystics called Shamans. The Shamans guided humanity, but, as the influence of the Warp grew (note that the Chaos Gods themselves were still dormant at this time), they found that they were dying-out, and their reincarnation abilities were beginning to deteriorate due to Warp Predation. Recognizing Mankind's need for guidance, they took poison and "died as one", which allowed their souls to collect and reincarnate all at the same time, and escape the predatory spirits of the Warp.
At first, the Emperor tried to simply "guide" Humanity, manipulating it from behind-the scenes to avoid the paths of Chaos. However, as he did this, the Chaos Gods became more and more aware of his actions and began to wake. Each God opposed the Emperor:
- Khorne woke first, and several wars erupted across Terra to Herald his awakening
- Tzneetch would wake next, after which political intrigue and schemes would come to light and cause huge strife
- Nurgle would awaken next, and a huge plague spread across the planet
All of these are predicted (but not entirely sourced) to have occurred within the 40K Terra's "Medieval" Period but have extended up until the Unification Wars, the conclusion of which decreased the influence of the Ruinous Powers in humanity by unifying Humans into one purpose: the Great Crusade, after which Horus betrays the Emperor and 40K history is born.
However, it wouldn't be 40K if there wasn't another story that casts doubt on the canonicity of the Shamans...
Vengeful Spirit (2014)
This is the story that you have heard referenced in the comments on the question. In Vengeful Spirit, the Emperor and Alivia Sureka travel to Molech and enter a Gateway to the Realm of Chaos. Here, the Emperor makes a pact with the Chaos Gods where he gets power in return for spreading Chaos worship throughout Humanity, but immediately reneges on his end of the bargain and becomes the Anathema.
Of course, this has some inherent flaws:
- Anything going into the Warp has to have a Gellar Field Generator (or the favor of the Chaos Gods) to stand a chance of making it out without annihilating. Now, the Emperor may have been able to do this after the bargain was made simply on account of his psychic strength, and it is possible that the Chaos Gods allowed him access to their sanctum, but it is not very feasible that Alivia Sureka, even a Perpetual as she was, would have been able to survive this.
- This tale also implies that the three Chaos Gods were already awake before the Emperor became the Emperor, and thus should have had no problem running-over Humanity without the need for a bargain with the Emperor.
- For beings known to be able to see the future, this seems remarkably short-sighted. This, in-particular, questions the purpose of Tzeentch, because how can a god of intrigue and plans ever hope to succeed if he is incapable of seeing such a short distance into the future. Of course, this may have been, as /tg/ would say, "Just as Planned," but considering the amount of hassle the Emperor has been to Tzeentch, this again seems unlikely.
- It still doesn't explain the "origins" of the Emperor. It talks about something the Emperor did, but does nothing to explain how he got to be The Emperor in the fist place.