A large series of 2-arylchromen-4-ones containing from 1 to 3 fluorine atoms or a trifluoromethyl group in the structure was synthesized by condensation of fluorinated 2-hydroxyacetophenones with benzaldehydes in an alkaline medium and subsequent oxidative cyclization of the resulting 2'-hydroxychalcones by action of I2 in DMSO. The cytotoxicity of the obtained compounds was studied in glioblastoma cell line, SNB19, and in a monkey-derived normal kidney epithelium cell line, Vero. In addition, antiglycation activity of the obtained compounds was evaluated. The inhibitory activity of some fluorinated 2-arylchromen-4-ones against acetylcholinesterase, butyrylcholinesterase and carboxylesterase as well their primary antioxidant activity in ABTS and FRAP tests were investigated. Screening of the synthesized compounds for their inhibitory activity against influenza A virus A/Puerto Rico/8/34 (H1N1) in the MDCK cell culture revealed that fluorinated compounds 32, 31 and 39 showed manifest antiviral effects (with IS = 57, 38 and 25 correspondingly) that makes this series of new biologically attractive fluorinated heterocycles promising for further development and in-depth study.