I'm not completely sure if this is where this kind of suggestions should go, but here goes nothing:
In the evolution screen marking with a Pokéball icon the Pokémon we already have at least one in the Pokédex. Having to check the Pokédex to know if we already have an evolution or not is annoying.
In the Pokémon selection screen make the fainted ones more easily distinguishable from the selectable ones. One example could be adding a fainted class to the slot and some CSS code like the one in the following block, because just having just the line-through isn't visible enough.
Add the viewport meta tag to the HTML of the pages with the width and the initial scale. I don't expect this to auto-magically fix all the problems on mobile, but the way it is right now only the map is mostly usable without lots of zooming and scrolling (at least in portrait orientation, because in landscape orientation the Battle button of the wild Pokémon is out of the screen and impossible to click)
<meta name="viewport" content="width=device-width, initial-scale=1">
In the change team screen (and probably others) when using the search it only autocompletes the name of the Pokémon species if we have the normal one. I only have a Shiny Lapras and if I write Lapras in the search box Shiny Lapras is displayed, but if I try to write only Lapras the suggestion box says "No Pokémon Found". It should suggest Lapras the same way it suggests Shiny Lapras to prevent typos when trying to search for all the variants.
In the Manage Your Pokémon Team menu (and probably others with the same format) the padding is in the ".menu-tab-selected" and ".menu-tab" classes, which makes only the text of the link clickable. If the padding is set in the ".menu-tab-selected a" and ".menu-tab a" it would have the same display but with all the box clickable.
The explore button links to https://www.pokemon-vortex.com/map-select/, which is a redirect to https://www.pokemon-vortex.com/map/live. It would probably be better if it pointed to the correct link directly.
There are probably more things than these that could be done to improve UX/UI, but these are the ones that came to my mind that slightly annoyed me while playing the last few days.