As a standard sample for measuring thermal conductivity for an Aluminum, is a sample of diameter 3 mm and height of 6 mm can be considered as a standard or the diameter should be increased?
Laser flash analysis (LFA) works well for samples in the form of plates, i.e., with a thickness much lower than the diameter. In your case, you are in the opposite situation, so you may have edges effect with so low diameter. LFA is very sensitive to heat losses through the edges of the sample, from where the need to have sufficiently large samples (typically 10 mm or more, depending on the sample holder). Therefore, I would not be confident in the results obtained with such sample geometry.
Consider the characteristics of your laser: Beam diameter, wavelength, power, dispersion and aangle of incidence. Beaams with larger diameters and dispersion in transit will necessitate larger surface on the sample.