Blazars are a class of active galactic nuclei (AGNs) known for their very rapid variabilty in the high energy regions of the electromagnetic spectrum. Despite this known fast variability, X-ray observations have generally not revealed variability in blazars with rate doubling or halving timescales less than approximately 15 min. Since its launch, the Swift X-ray Telescope has obtained 0.2-10 keV X-ray data on 143 AGNs, including blazars, through intense target of opportunity observations that can be analyzed in a multiwavelength context and used to model jet parameters, particularly during flare states. We have analyzed this broad Swift data set in a search for short timescale variability in blazars that could limit the size of the emission region in the blazar jet. While we do find several low-significance possible flares with potential indications of rapid variability, we find no strong evidence for rapid ($<$15 minutes) doubling or halving times in flares in the soft X-ray energy band for the AGNs analyzed.