ESTA and Application for residency visa

My partner will be coming to UK soon and we will be married. She is a US citizen and we already have a UK Fiance Visa.

Once we are married in UK we intend to apply for FLR(M) for her. Around the same time we intend to submit my US I-130 papers.

Once the I-130 process is started, what, if any, impact will there be on my US ESTA which is valid until June 2018? Does my ESTA become invalid?

I do not see any reason why your ESTA should be invalid till you have a letter from USCIS stating that you have another US immigrant visa.