Yes, you will be able to get him/her an EEA FP. I have done EXACTLY this.
I was British and Irish from birth. I renounced British citizenship in April and my civil partner received his EEA family permit in June. We will travel back to the UK in July (we live in China at present). The family permit was issued quite quickly (8 days including weekends/one 1-day public holiday).
I had sought advice from the Home Office before renouncing. They said that renunciation of British citizenship means that they will not treat us as British at all.
Just remember that it's hard to get British citizenship back if you renounce it for this reason. I have been told by the Home Office that I could only be considered for resumption under the discretionary power held by the Home Secretary (not that I care!). Also remember that the UK might leave the EU. This may cause problems (of course, no one knows yet). Also: you might want to investigate the Surinder Singh route (if you have worked in another EEA country).
Any questions just fire away... or see here:
http://www.immigrationboards.com/eea-ro ... 13833.html