The Eight Mansion (Ba Zhai) system of Feng Shui identifies good and bad sectors in the home according to the house's magnetic orientation. In Ba Zhai, there are four auspicious directions and four inauspicious directions within each home.
The Flying Star system, as you have learned, includes the factor of time in its calculations to determine whether a sector of a house is auspicious or inauspicious.
Sometimes, a sector may be identified as auspicious from an Eight Mansion perspective, but inauspicious from a Flying Star perspective, or vice-versa. Does this mean that the Feng Shui formulae contradict one another? Not really, it just means that the interpretation must be carried further.
Here is an example: Suppose you have a sector that has an 8-White Facing Star in the Flying Star system, indicating that it is good for financial success. The Eight Mansion system, however, indicates that the sector is Liu Sha (Six Killings), which means that it promotes the presence of malicious, backstabbing people in your life. Is this a contradiction? No, it means that you have the potential to excel in your career and make a lot of money, but this success can promote jealousy and backstabbing behavior in the people around you.
At this point, you need to decide which scenario is more important to you, and use the sector accordingly. The effects of Eight Mansion Feng Shui tend to be longer-termed and more stable, but take longer to have an effect. Flying Stars generally bring faster results, but they don't last as long. As a rule of thumb, if you are renting a property for the short-term, Flying Stars is probably the better system to use. It is also better to use Flying Stars if you need results quickly. On the other hand, Eight Mansion is perhaps better suited if you are a property owner and are "in it for the long haul". You can also use both systems together if you are careful and methodical about it.