T2-weighted fluid-attenuated inversion recovery (FLAIR) magnetic resonance imaging (MRI) scans are important for diagnosis, treatment planning and monitoring of brain tumors. Depending on the brain tumor type, the FLAIR hyperintensity volume is an important measure to asses the tumor volume or surrounding edema, and an automatic segmentation of this would be useful in the clinic. In this study, around 5000 FLAIR images of various tumors types and acquisition time points from different centers were used to train a unified FLAIR hyperintensity segmentation model using an Attention U-Net architecture. The performance was compared against dataset specific models, and was validated on different tumor types, acquisition time points and against BraTS. The unified model achieved an average Dice score of 88.65\% for pre-operative meningiomas, 80.08% for pre-operative metastasis, 90.92% for pre-operative and 84.60% for post-operative gliomas from BraTS, and 84.47% for pre-operative and 61.27\% for post-operative lower grade gliomas. In addition, the results showed that the unified model achieved comparable segmentation performance to the dataset specific models on their respective datasets, and enables generalization across tumor types and acquisition time points, which facilitates the deployment in a clinical setting. The model is integrated into Raidionics, an open-source software for CNS tumor analysis.