Hi Tina,
Welcome to FT.
Im wondering whether I can buy a standard economy ticket at JAL and then use my Flying Blue points to upgrade to a business class?
There is a general view that this is not a good use of miles, because you have to buy a full-fare economy ticket, and they are tremendously expensive. It is usually better to buy a business ticket with your award miles, on which you would have to pay taxes. The best value awards are promos. The straightforward answer to your question is 'yes' - but not recommended.
Also.... can you transfer Flying Blue points to JAL points? If so what is the site or contact details?
I would be very surprised if you could do this. These are loyalty programmes, and there would be no concept of loyalty if we could simply transfer miles. You might be able to get a status match if you are at an elite level, but this would not help with award style miles. Someone else may have come across such a transfer, but similar questions have been asked many times in this forum and I have never known anyone get a transfer of miles.
Where and when are you flying? Maybe the current promo awards could be of use to you?