>>35353005If I had to guess, I'd say
Umbreon > Jolteon > Vaporeon > Espeon > Flareon > Sylveon > Glaceon > Leafeon
However, I wasn't satisfied with that sort of answer, so I did some light research.
In terms of Google search results, each of the eeveeloutions had the following number of hits.
Jolteon: 3.1MM
Flareon: 3.3MM
Vaporeon: 3.91MM
Umbreon: 5.89MM
Espeon: 4.21MM
Glaceon: 2.73MM
Leafeon: 2.55MM
Sylveon: 3.79MM
I decided to take it a step further and check out hits for both Pixiv and Deviantart, because I'm a faggot I guess and I wanted to see if I could get a good feel for how the western and eastern side of the fanbases might differ in taste.
Jolteon: 3640, 70,134
Flareon: 5473, 75,766
Vaporeon: 1403, 80,315
Umbreon: 5570, 202,272 (wow what a surprising result from devianart)
Espeon: 4273, 113,181
Glaceon: 5917, 82,090
Leafeon: 4033, 66,387
Sylveon: 4385, 64,984
And for fun the amount of hits on the Rule34 Booru
Jolteon: 1536
Flareon: 1639
Vaporeon: 2177
Umbreon: 3798
Espeon: 1838
Glaceon: 2405
Leafeon: 1517
Sylveon: 1861There was also a Pokemon popularity poll from 2016, but I chose to ignore it as it had some obvious newmon bias.
So, taking this info into consideration both general hits and amount of fan art, we can probably say, in terms of popularity, it probably goes
Umbreon > Espeon > Flareon > Vaporeon > Glaceon > Jolteon > Sylveon > Leafeon
Might post some more thoughts in another post.