From your question, I'm unclear if you're asking why they use flashlights even when there are lights on, or why they use flashlights instead of using the lights.
The latter is easier to answer. They want to research and document the crime scene exactly as they found it. From Crime-Scene-Investigator:
Documenting crime scene conditions can include immediately recording
transient details such as lighting (on/off), drapes (open/closed),
weather, or furniture moved by medical teams. Certain evidence such as
shoeprints or gunshot residue is fragile and if not collected
immediately can easily be destroyed or lost. The scope of the
investigation also extends to considerations of arguments which might
be generated in this case (suicide/self defense) and documenting
conditions which would support or refute these arguments.
They are looking for a single fingerprint, or strand of hair. Even turning a light on or opening a curtain could erase evidence. Therefore, they document the entire scene first by taking pictures, checking for all prints and using only their flashlights rather than other light sources.
Think of the season opener to Series 5, when Greg failed his entrance test to become a CSI for using a toilet at a crime scene - risking corrupting the crime scene and destroying evidence.
If however you were asking why they use flashlights in addition to the lights in the room, I think Paulster2 in his comments above has answered perfectly. The additional light source provides a greater level of illumination and clarity and makes it easier to find things.