Can we get our own flat while getting job seekers allowance?

I wouldn't consider moving until you are both in secure employment. It's not just getting a flat, it's all the other expenses, food and utilities, council tax etc that you need to think about. You will also need a deposit to rent a private property which is often a month's rent in advance, plus you'll need your first month's rent as well. It's extremely unlikely that a private landlord would rent to you whilst you are both on JSA; on such a low 'income' you would likely be unable to meet your living expenses. You can apply to go on the housing list with your local council/housing authority but the lists are extremely long and a childless couple who have somewhere to live (even if it's your mum & dad's house) will be low priority. I understand that you want to live together but in your current cirstances it's best to wait until you both have jobs and have saved enough money for a deposit, moving expenses and your first month's rent. DSS stands for Department of Social Security but it's not really called that anymore!