I don't see a way to setup bbcode's with html though. Am I missing something? If there isn't a way, is there another way of achieving this with the existing system, or can we get html support for bbcodes?
Yup, you absolutely can do it, but I absolutely would not recommending doing it the phpbb way. I honestly have no idea why it'd be done so convolutedly.
Instead, You could do the old HTML way:
For the Search String:
/\[blink](.*)\[\/blink]/si
For the replacement string
<span style="text-decoration:blink">$1</span>
The replacement string should be the HTML you want it to turn into, you just need to be aware that the Search string is perl regular expression, which aren't obvious without a little practice.