...,says I am entitled to connect 3 devices, but in the app settings am only at 2 my phone and computer ...
You can check out what's connected to your Dropbox account in security setting (scroll down). If within device section are listed device(s) not supposed to be there, just wipe it/them out (left just your phone and computer).
... the printer is asking for a dropbox address code to enter into the printer? ...
Most probably your printer is asking for authentication code. If so, such a code you should receive on confirmation your printer connect to the Dropbox account. Exact steps to do this could vary and depend entirely on your printer supplier. Check out the printer documentation (there could be more info) or ask your printer's supplier. 😉
Hope this gives direction.
From your last words, sounds like you are not sure what you are asking for! At the beginning is your printer support cloud work (especially with Dropbox) or not?! If there is no such support, what we are talking about? Dropbox application generally doesn't support third party devices. (at least not directly)
... The printer is asking for a code from dropbox to printer, not printer to phone?! ...
Usually, when another service (third party application or device, including device specific application on phone, for example) going to connect to your Dropbox (or other) account, there is a process of authentication (you confirm this access). Frequently used way is confirmation with a security code (despite not the only, but one of supported from Dropbox). Some devices could integrate such features internally, others use device specific (mostly provider specific) mobile applications to do this. Find out if your device or associated mobile application have such a feature. If there is, read associated documentation (or support, if any) how to use it.
Alternative could be export scanned document from your printer (seems MFD) application to Dropbox application. This should always work without additional authentication, codes, etc. Just one more step (transfer between applications) when you save a scan to your Dropbox account every time. 😉 That's it.
Hope this clarifies matter.
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