What's the difference: 一点 or 一点点? I feel kind of silly for asking because I doubt it's a huge difference. However, I can't seem to find any answers online. I understand that both mean a little as in 我会说一点缅甸语 or 请说一点慢 。

Is there a significant difference (regional, cultural, grammatical, preferential, etc) ?
一点 means “a bit”.
一点点 means “a teeny weeny bit”.
So if you use 一点点, the intensity of the thing you are talking about will be much milder.

我会说一点英语。(I can speak a bit of English.)
我只会说一点点英语。(I can only speak a tiny bit of English.)

I think 一点VS一点点 is analogous to pequeño VS pequeñito in Spanish.
By the way, your second example should be 请说慢一点.