I dont think you should.
* It's wise for a friend not to date a friends ex boyfriend/girlfriend, but 'ex' means that person is single and can date whomever he/she wishes to date. If you still have feelings for your ex then your friend isn't much of a friend and you should tell them so.
I honestly wouldn't do it, dating or going on a date with a friend's ex is a terrible thing to do, it's like a subconscious sort of friend-code where we don't date or do anything with a friend's ex.
First, do they know that he is your ex- boyfriend? If they do then that doesn't mean they are not a true friend. You dumped him (or he dumped you) right? Then she(your friend) can date him if she wants to. You and your ex are over, so why does it matter who comes and dates him next?
But if you really like him, and not only trying to make your ex jealous. Then love never comes second. Date him, only under the right terms.
'Ex' means you are no longer in a relationship with that person so you are as free as your ex boyfriend to date anyone you choose to date. If you are really attracted to your ex's friend then when your ex is not around ask his friend out to a movie or a favorite spot you may hang out at.
You date her best friend
definitely not
If they date, you will just need to let things run their course. Since you gave your blessing, you can't be mad at your friend or the ex.
Ask her if shes ok with it.
date her BEST friend.
appologise and arrange a date