Office suite with spell check and dropbox sync for iOS?
If I am right you are asking about the red squiggly lines that appear under mis-spelt words? 


Pages does this and on iOS 11 the Dropbox sync is seamless with files integration
Word from Microsoft does the same as Pages on iOS 11 but isn’t free for devices with a screen size above 10.1 inches (so the two largest iPad Pro are paid editing only). You need to bring some form of O365 subscription to get all the features on all screen sizes. 


The spell check is a native feature within iOS, rather than the app. So if you type in the app you will get the auto correct.

You can use Pages to spell check as this has the red lines but you can't put back into drop box.

QuickOffice does sync with Dropbox, but doesn't spell check, (a feature which may be added soon) Documents to Go only offers dropbox sync with it's premium version which was misled by it's iTunes description.