READ REAL BOOKS.
No substitute for it. Far easier to learn and remember new words in context and far, far more fun.
Only tutor your child with 40 quid flashcards if you are determined to put your child off English for life.
Apart from reading, there are other fun ways to increase vocab - play Scrabble, Boggle or the add-a-letter game (person A says a letter, person B adds another letter, person A the next etc. The aim is not to finish the word. But you must have a real word in mind at all times, or you lose. So eg person A says P, person B can't say I or A because that would finish the word, so says U, making PU. Person A can't say T because that would make PUT, or S, because that would make PUS and so lose the game (even though there is a longer word, PUSH). So says R, thinking of the word PURE. Person B can't think of any other real word they could make that begins with these letters, so either says E and loses the game because they finished the word, or says "challenge", hoping the other person didn't have a word in mind at all. Person A can then say "PURE", meaning Person A has won.
Cost: free.
Can be played anywhere, with no equipment. Great for practising compound words (can play the harder version, where letters can be put at the front OR back of existing letters, thus testing prefixes as well as suffices, once you have the hang of it). Also good for spelling and visual memory.