How to sign out of iCloud on iPhone and Macbook without having access to rescue email and with Find my iPhone and Find my Mac turned on? I have an iPhone 7 Plus and a Macbook Pro 15" 2014.
I was trying to make calls from Facetime Audio on Mac from my iPhone. My Apple ID was asked on Facetime on Mac. I entered my details and it told me that your account has been locked due to security reasons.
So please enter the answer to your security questions which I don't remember. I entered twice and it greyed out this option of security questions. Now the only thing I was left with was to email myself (through Apple) the reset link so as to reset the password. But here's the bad thing that happened to me: The email that I was using with iCloud and Apple ID was my previous employers email and since I left the job, I couldn't access it anymore. So I couldn't get the reset link. Same thing happened with me on both iOS and Macbook.

Now I can't have iCloud sync between both these devices, can't download anything from the appstores on both the devices. I tried signing out of iCloud on my iPhone (and on Mac) but since my Find my iPhone(Find my Mac on Mac) was ON, it didn't let me sign out. I backed up my iPhone and tried erasing all my iPhone so that I could log in with some new Apple ID but since FInd my iPhone was ON, I couldn't erase my device either. Also tried restoring through iTunes, but all in vain since Find my iPhone was ON.

What should I do now? My Macbook and my iPhone are my primary devices and I can't live without iCloud syncing on.
First of all, the comment by Patrix is an excellent way to start. I've helped many users by using the various options there (sometimes having to add other security email addresses, calling Apple Support, etc). This process may or may not be extremely frustrating - I've seen users sort things out pretty quickly, and others who have had to wait days for Apple to call them back once everything was sorted.

However, another option which may or may not be palatable to you is to just contact your previous employer. 

About six weeks ago I came across a very similar situation, except in their case it was an old email address from an ISP they were no longer with. After some negotiation the old ISP agreed to recreate the email address at their end for one hour and set it up to autoforward to the user's current email address. During that hour the user was able to access the emails from iforgot.apple.com and change their email address etc.

Of course, in your case it may be a case of being allowed access to your old email (either because it still exists, or because they've recreated the address for you). Or they could set up an autoforward as happened in the above example.

If this isn't an option, then iforgot.apple.com really is your only option.