Transfer my data.

Well you could, but the real question is whether your Kenwood would read it, and I have no idea about that.

So far it won't.

What, you can't transfer the data or your Kenwood can't read it? If the latter you should contact Kenwood.

It won't transfer, when I hit the transfer button a box pops up, but nothing is in to select.

Does your device show in BaseCamp?  If not then hitting transfer won't work. I suspect you need to use the export function to export a gpx file and then transfer that to your device.

Nothing seems to work, o well.

Sorry but when you say 'nothing seems to work' that doesn't help us to help you.  At what stage is it not working?  Have you been able to export the relevant gpx file from BaseCamp?  Were you able to transfer it to your Kenwood?  If you were I assume by 'nothing seems to work' you mean your Kenwood doesn't appear to use the gpx file?  If that's the case you need to contact Kenwood, it may be something they can help you with. Alternatively you may need to create a folder on the SD card called Garmin/GPX and place the gpx file in that, see this which talks about POIs but explains how to create the folder and then how to get your Kenwood to install the data.

https://support.garmin.com/en-GB/?faq=IAp7hTXUvuArGnCF8n73A7

I downloaded the gpx file, and put it in the Garmin main folder, also put it in the JVC, Pnx, SID folders on the SD card. When I try send to device the dialog box will pop up, but no device will show in it.

Where do I need to create the folder at?

As I posted above, try Garmin/GPX.  If that doesn't work you'll need to contact Kenwood, it may not be possible or you may need to use the link I posted to turn your gpx file into a POI file.