Copper concentration is becoming more difficult because remaining copper ores are more complex and of finer copper mineral grain size, making copper minerals harder to float because of the fine particle size required to liberate the valuable species. The purpose of this work was to study the flotation behavior of fine copper sulfide ores at different conditions of agitation and aeration. The experimental campaign was carried out in a laboratory Denver-type flotation cell of 1 L volume modified to be operated with forced air that allows decoupling air flow rate and agitation speed. Four ore samples from Chile were used, all of them containing copper sulfides such as chalcopyrite, bornite, chalcocite, and tennantite, but with varying grain sizes and compositions. Preliminary flotation tests for establishing the flotation conditions of grinding size and collector dosage were conducted before the kinetic flotation tests that were carried out at different agitation speeds varying from 900 to 1300 rpm for gas flow rate ranging from 1.6 to 7.2 L/min. The flotation products were analyzed by ICP-MS and MLA (Mineral Liberation Analyzer). The results showed that high agitation speeds with corresponding air flow rates resulted in better recovery than moderate agitation speed and air flow rate, and an excess in gas flow rate resulted in bad performances. The flotation rates of the fine copper minerals were improved despite the different improvement rates among the fine size fractions. The impact of these operational variables, however, was different when comparing the results for the four ore samples. While it was found that the order of floatability in the four samples was the same, that is, chalcocite > tennantite > bornite > chalcopyrite, the kinetic constants of the copper minerals in the samples were different, indicating that mineral composition in the sample affects the flotation kinetics.