Greenwich Park is a great place to skate in London, and luckily it is also really easy to get to with multiple travel options from destinations within London, including:
Cutty Sark station - it is only a short walk from the station to the park (of course you still have to trek up the steep hill :).
Greenwich station - follow the signs to the Park.
Connecting trains depart from Cannon Street, Waterloo, London Bridge and Charing Cross and go to Greenwich, Maze Hill and Blackheath.
North Greenwich - Jubilee Line (then catch the 188 bus to Greenwich Park gate.)
53 Trafalgar Square - Plumstead
54 Woolwich - Elmers End
177 Thamesmead - Peckham
180 Thamesmead - Lewisham
188 North Greenwich - Russel Square
199 Canada Water - Catford
202 Crystal Palace - Blackheath
286 Greenwich - Sidcup
380 Lewisham - Woolwich
386 Greenwich - Woolwich
You can take riverboats to Greenwich Pier from Westminster, Embankment or Tower Piers.
There is also quite a large car park area open to the public with the entrance on the Blackheath side of the park.
As a final option you could always skate to Greenwich Park. I have heard of skaters coming from all over London to Greenwich Park on their skates. When coming from the City, you can skate down through the Isle of Dogs, through the Greenwich Footpath and be at the gates to the park before you know it. But remember you still have to skate up that hill... so save some energy!!
Below in blue is the route from either the Cutty Sark DLR station or Greenwich DLR station to the park.