EEA resident permit

I am resident of the UK but Russian citizen , married to the British Citizen ,got resident permit . Can I exchange my resident permit for the EEA family member resident permit which will allow me travel to Europe visa free .

No, because the EEA family member resident permit is only for family members of other EEA citizens, not of British citizens.

But as a family member of a British citizen, you could get a Schengen visa free. You can, in theory, travel visa-free if you are travelling with your British spouse or travelling to join her elsewhere in the UK. But you will need to carry around documentation to prove your relationship to her.

As the spouse of a British citizen, you will be eligible for citizenship immediately after getting ILR. After that, you should be able to travel visa-free across the EU.