The Solar Flare Index is regarded as one of the most important solar indices in the field of solar-terrestrial research.It has the maximum effect on Earth of all other solar activity indices and is being considered for describing the short-lived dynamo action inside the Sun.This paper attempts to study the short as well as long-term temporal fluctuations in the chromosphere region of the Sun using the Solar Flare Index.The daily Solar Flare Index for Northern,Southern Hemisphere and Total Disk are considered for a period from January 1976 to December 2014(total 14 245 days)for chaotic as well as periodic analysis.The 0-1 test has been employed to investigate the chaotic behavior associated with the Solar Flare Index.This test revealed that the time series data is non-linear and multi-periodic in nature with deterministic chaotic features.For periodic analysis,the Raleigh Power Spectrum algorithm has been used for identifying the predominant periods within the data along with their confidence score.The well-known fundamental period of 27 days and 11 years along with their harmonics are well affirmed in our investigation with a period of 28 days and 10.77 years.The presence of 14 days and 7 days periods in this investigation states the short-lived action inside the Sun.Our investigation also demonstrates the presence of other mid-range periods including the famous Rieger type period which are very much confirming the results obtained by other authors using various solar activity indicators.