Laminar flame speeds of ammonia with oxygen-enriched air (oxygen content varying from 21-30 vol.%) and ammonia-hydrogen-air mixtures (fuel hydrogen content varying from 0-30 vol.%) at elevated pressure (1-10 bar) and temperature (298-473 K) were determined experimentally using a constant volume combustion chamber. Moreover, ammonia laminar flame speeds with helium as an inert were measured for the first time. Using these experimental data along with published ones, we have developed a newly compiled kinetic model for the prediction of the oxidation of ammonia and ammonia-hydrogen blends in freely propagating and burner stabilized premixed flames, as well as in shock tubes, rapid compression machines and a jet-stirred reactor. The reaction mechanism also considers the formation of nitrogen oxides, as well as the reduction of nitrogen oxides depending on the conditions of the surrounding gas phase. The experimental results from the present work and the literature are interpreted with the help of the kinetic model derived here. The experiments show that increasing the initial temperature, fuel hydrogen content, or oxidizer oxygen content causes the laminar flame speed to increase, while it decreases when increasing the initial pressure. The proposed kinetic model predicts the same trends than experiments and a good agreement is found with measurements for a wide range of conditions. The model suggests that under rich conditions the N2H2 formation path is favored compared to stoichiometric condition. The most important reactions under rich conditions are: NH2+NH=N2H2+H, NH2+NH2=N2H2+H2, N2H2+H=NNH+H2 and N2H2+M=NNH+H+M. These reactions were also found to be among the most sensitive reactions for predicting the laminar flame speed for all the cases investigated.