Not exactly fleas, but maybe close enough that the difference to you would be pedantic: let's talk about lice.

By sequencing the mtDNA of body lice, scientists have formed some theories about human history, namely the development of clothing.

There is no archaeological evidence for the invention and widespread adoption of clothing. Such evidence is likely too old for us to find. But, we can turn to evolutionary science of bugs to help.

We know that the human body louse is distinct from the human head louse in that the latter lives literally on the human (the scalp), whereas the former lives on clothing despite feeding on humans. Thus, the theory goes, we can get a glimpse into the development of clothing the more we learn about body lice.

By studying its mtDNA, scientists have determined that the body louse evolved somewhere between 30,000 and 110,000 years ago. This gives us a window for the development of clothing, since the body louse needs clothing as a habitat.

In considering the possibility that clothing significantly predates the evolution of the body louse, this study (linked below) notes, "While we cannot exclude this possibility, the colonization of a new ecological niche usually occurs rapidly after it becomes available." It is understood by scientists that parasites evolve much faster than their hosts do, given the short-lived (and rapid reproductive) nature of parasites. (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2957397/) So, it is believed that it did not take long for head lice to evolve into body lice.

Moreover, scientists studying the body louse can weigh in on whether archaic humans (e.g., Neanderthals) wore clothing: "Since modern humans and archaic humans such as Neandertals diverged about 250,000–500,000 years ago, in order to associate clothing with archaic humans, clothing would have had to exist for hundreds of thousands of years before the origin of body lice, which seems improbable." In other words, there isn't an identified reason why the relatively fast evolving head louse would evolve so long after a new change--clothing--is introduced to their host and environment.

The study also takes note of the development of human tools that might coincide with clothing. Although we don't have direct evidence of the invention and adoption of clothing, we do have an archaeological record of these tools over time. Although it's impossible to know when these tools themselves were invented, they can serve as tests against the theory that body lice and clothing developed at roughly the same time. We have identified the earliest needles we've found as around 40,000 years old. This coincides with the evolutionary development of the body louse (30,000-110,000 years), and seems to support at least a 40,000 year old date for the development of clothing.

Lastly, the study reveals that there is greater diversity among body lice in Africa than all of the rest of the world combined (at least, as observed by this study). This suggests an African origin for body lice. This is in line with greater diversity among human populations within Africa than without. Importantly, this supports the out-of-Africa theory of human evolution and migration, and would suggest that clothing was developed and adopted by humans before said migration occurred.

Although this doesn't shed light specifically on fleas or the struggle humans had with battling them, hopefully you find this interesting.

Most of this is found in this paper: https://www.cell.com/current-biology/fulltext/S0960-9822(03)00507-4