The stock brompton foam grips might be giving one a sense of flex. I have an M-Type and I do notice some flex on the bar but nothing that bothers me. After replacing the stock foam grips with ergons, it felt like the bars flexed less. Again I was not bothered by the flex even before I replaced the foam grips. Another thing to consider is the "suspension"... the regular suspension block has more give than the firm one.

I would categorize the brompton's ride as springy not flexy... this is in comparison to my aluminum and carbon framed road bikes. My aluminum bike's ride borders on being harsh, the carbon bikes are smooth but firm, the brompton is springy... just right for my commute.