I'd probably put these in a completely separate discussion, since this series is so different ^^ But AshxMallow I could see! Moreso than AshxLillie, somehow.
As for the original series, I think I'm leaning towards AshxDawn c: They were just superbly bestfriendly and would have been equal partners, while the May and Serena relationships seemed a bit too much leaning towards the girls adoring Ash as a mentor or senpaiii. buuut I might remember things wrong tbh haha. I haven't watched all of the Sinnoh arcs and it was a long time ago even!
I put Sun&Moon at 6 to 8 because they're the newest relationship's from the series. Until we learn more about them, its hard to place them higher than the previous Generations and even determine a proper order. The reason I put Lillie above Mallow right now though is because Lillie has had three Episodes in which she has interacted with Ash and his Pokemon. You have Episode 8 when she first get's the Egg(and she breaks her fear of touching anything), Episode 14 where she meets Shiron(aka Snowy) for the first time and Ash is dragged off by Mallow to follow her(and ultimately saves her) and Episode 30 where she and Ash trade partners(Pikachu is one lucky guy). From a symbolic standpoint, Ash has given her the strength and motivation to break her fear and she will hold him in high regard for doing so. Whether that translates to a romantic feeling I don't know but Serena turned Ash's act of fear breaking into a romantic crush. Of the three Pokegirls, Lillie is technically the lone Pokegirl if they were to have gone by the game script with Mallow and Lana acting as Trial Captains.
As for Mallow, I can see where you're coming from. Mallow's attraction to Ash started from Episode 1 when she bulldozed him with the Tauros she was riding. Then there is the body language, Bounsweet pheromones(which know no boundaries), getting semi-jealous in Episode 13, giving him first dibs at Food in Episode 18, the ground ball scene in Episode 28(I didn't really notice it until I watched reviews. Respect girl... Respect...) and the infamous "Pants" scene in Episode 32 where Mallow got more than she bargained for. I just think that with her Deredere archetype(which is debatable but frankly I think it fits), she will fight for Ash's heart but won't care one way or another since her true goal is to see to it that everyone around her is happy(hence cue all the Episodes and corresponding scenes where she looks after Lillie and helps Lana. Even goes out of her way for Sophocles but I haven't really noticed her giving a damn about Kiawe(largely because he doesn't need it).
As for those shipping AshxLana... all you've had to go on so far is Episode 5 and 16. With Episode 33's Thumbnail... damn the symbolism be real. First real instance in my mind where you could argue that ship has a shot.
As for AshxDawn, that ship grew from the fact she did cheerleading(which is infamous) during Ash's Gym Battles, Ash returning the favor by watching all of Dawn's contests(didn't do that for May), Lyra asking Dawn about who she was going to marry and referencing Ash and noting how good of a candidate he was(and Dawn never really considering it until then) and other instances that implied the two had feelings for one another.
AshxMay was more Master/Apprentice than romantic. There were indeed sparks but Drew ship has a stronger argument with the flowers and parent nudge.
AshxSerena was a built-in romantic ship. Childhood meeting that had Serena blushing at every opportunity Ash said something complimentary or her crush being brought up by Miette or Shauna. Even Bonnie knew about it and burned both Ash and Clemont in Episode 80(my favorite scene). The reason people really ship it is because Ash did notable things: Asking her to join the group, giving her a gift voluntarily, using said gift to change her appearance(which had never been done before in the series), Ash choosing Serena's dream over his(I forget the Episode but it was prior to XYZ 19/20 Master Class Episodes) and slowly but surely realizing through that dense skull of his that he not only had a good friend but a lifelong partner. Serena just didn't want to end up in the friendzone and acted on her romantic feelings in the finale(which every Amourshipper had wanted her to do and every shipper prior to that had wished had happened for their Pokegirl). Plus, Japan is by far, the weakest country with regards to showing kiss scenes. Even the white flag French show more in their animated series for kids and its ironic since XY takes place in a French themed region.
