Is it permissible for someone suffering from constant seminal discharge (sals al-madhi) and flatulence to pray the obligatory prayer at home alone, and then go to the mosque to pray it with the congregation, and is there any legal basis for this?

The person afflicted with continuous flatulence is excused from attending the mosque. If you are not afflicted with this, then strive to perform the prayers in the mosque. If you pray at home and then go to pray a second time in the mosque, there is no harm, provided that you do not make this a habit, and your second prayer is considered a supererogatory prayer. It is not permissible for you to continue praying if your ablution becomes invalid.