Interesting, I saw reasons for several pronunciations.
(Sorry for leaving some 文言(ancient Chinese)because I don't know how to properly translate from ancient Chinese to English)
The origin of this word:《史记·卫将军骠骑列传》：
冠军霍去病既侯三岁，元狩二年春，以冠军霍去病为骠骑将军，将万骑出陇西，有功。
【集解】徐广曰：“骠，一作‘剽’” :骠 can be also written as '剽' piāo
【正义】《说文》云：“骠(biāo)，黄马鬣白色，一曰白髦尾” 骠 is yellow horse with write hair on head or neck, also said has a write tail
(Both 集解 and 正义 are famous comments on 史记)
And after looking up my dictionary, initially I think the answer is piào which means brave.
For 骑, qí means riding, jì means the person who rides horse.
以霍去病为骠骑将军，将万骑 (I simplified the sentence here)
means assigned 霍去病 as 骠骑将军, then commanded ten thousands of 骑(cavalryman)
I can't infer a certain conclusion which one should be chosen:
qí : the name is saying something about the person's riding
jì : it's 骑将军 who commands 骑(cavalryman)
Personally speaking, I think the later is more reasonable and the former is a bit meaningful.
In fact this question is somehow opinion-based because answering it requires interpreting ancient articles which is debatable.