The battery on my 2014 XK Convertible has run down till it is completely flat. I haven’t used the car for a few months but I still didn’t expect that. In the past when the battery has run low I’ve been able to give it an overnight boost through a trickle charger I had installed. However, this time that is not doing anything as the battery is completely flat. I’d really appreciate any suggestions from fellow owners who’ve experienced this or know a good solution. As far as I can see, I have two options. Do I try and jump start with another car/battery or buy a battery charger and try and get some juice in the battery? Thanks!

 

Third option: new battery. (Especially given your comment "In the past when the battery has run low...")
If you have AAA (and you should, with these cars), if you call for a jump very often (at least in cities) the person who comes will have a selection of batteries if you want to buy one. Or tell them that you might need a new battery and they'll bring one.
Or get your own AGM battery and install it.
Either way.... new battery.

 

^^^^^^^^^^^^
What he said

 

And that new battery will not be, definitely not be, fully charged. Given your history, it seems that you do not drive often enough or far enough to keep the battery fully charged. If you have a battery maintainer installed permanently, it should be used regularly (that means always) to eliminate this issue of low battery voltage.