Yes, I'm using Chrome Version 55.0.2883.87 m (64-bit) on a Windows 10 (64-bit) - all of the latest patches have been applied - with a GoDaddy hosted Office 365 subscription running all of the Office apps, including Excel, at the 2016 version level. I have cleared the cache and run Chrome in both regular and incognito modes. I'm still getting the same error within Excel which is logged into the same GoDaddy O365 account as are the web & PC based PowerApps and the web based Flow app. (Excel doesn't appear to have the ability to specify a PowerApp/Flow 'environment' but all of my PowerApp & Flow login's include the 'default' environment as a part of their execution context.
I have a 2nd environment defined which is where I was, 1st, able to access my, separate, premium Common Data Service subscription. I started exploring PowerApps/Flow sometime in December. At that time, I wasn't able to access CDS directly through GoDaddy as they don't support Enterprise level features. (I spoke with a support person at GoDaddy and he felt pretty sure that I wasn't going to be able to access CDS under GoDaddy due to the nature of their product offerings around Office 365.)
I noticed that there was a separate 'Sign-up' for premium services that I found on the Microsoft PowerApp website. I used it to setup my 'separate' trial of CDS. After doing so, I was unable to figure out how to access the CDS through my GoDaddy account within PowerApps. I came back at over the past couple of days and noticed that things seemed to have changed as my PowerApps account had a reference to access CDS. I attempted to do so from within my default environment but didn't get the CDS environment to build within it. Given that, I hunted around the PowerApp boards and found a CDS note that recommended using a different environment if connectivity/access issues seemed to be preventing the CDS from realizing itself.
I created a new environment and was able to get the CDS connection to initialize itself within it. It was within this separate environment that I 1st encountered this authentication issue. (The 1st evening when I successfully initialized the CDS, I was able to do everything including the MS Excel 'Open' function without error.) The authentication issue appeared the next day after I had to re-establish all of my connections to PowerApp/Flow with my GoDaddy credentials.
2 days ago, out of frustration, I went back to my default environment - I had seen a number of posts on this board related to various authentication issues that MS addressed by doing fixes in the backend - and attempted the CDS initialization again.
This time it worked. I have, since, switched over to using only the default environment. The authentication error message below was gotten a few minutes ago attempting to open up the Contact Entity using the 'Open in Excel' button.
By the way, I deleted and then re-installed the Excel Add-in for PowerApps at the same time, 2 days ago, in the hope that a fresh start might help.
***Error message from Excel 2016's PowerApp Add-in***

I had seen, in another post by you, that you might want/need a 'Fiddler' dump for such issues. I downloaded and installed the Telerik version of Fiddler and have played around with it to the point where I can save a 'secured' dump just in case you might want it.
Thank you,
Frank