Is there a way to convert Emirates Skywards Miles to either British Airways Avios or Delta Skymiles?
I'm a UK citizen and willing to get a new credit card if it would make the conversion possible.
It is sometimes possible to transfer airline miles from one programme to another, but is rarely a good idea. Typically it involves transferring to another programme such as a hotel chain and then from that to the other airline.
There is a form on webflyer showing how this is done, though I'm not sure how up to date it is. For example you can convert 10000 Hawaian miles to 20000 Hilton Hhonors points to 2000 Delta skymiles. There is no Emirates conversion path listed on that site.
Emirates list its partners including multiple airlines and hotels that Skywards points can be spent on and that is very likely to be the best way of spending the miles other than Emirates airline tickets themselves. It does list some hotel partners such as Marriott which might be useful for conversion purposes, but a quick search shows that these can only be used to book rooms rather than convert to hotel points.
The only transfer out partner listed on that page appears to be Heathrow Rewards (search for convert in Emirates partners page above). You can spend Heathrow Rewards points at airport shops in Heathrow. You cannot use Heathrow Rewards points gained from Emirates to transfer out to another airline programme such as avios.
Points converted from Skywards Miles cannot be converted into Avios or other mileages offered by the Heathrow Rewards Programme.