Akko And Diana
Some people ship Akko and Diana for many reasons, including but not limited too, the fact they both inspire each other to be who they are near the end of show, the fact that they were the main people to stop the missile, they both adore Chariot, both went to Luna Nova because Chariot did, Diana confessed her love to Akko under a posion, etc. Their ship name is Diakko.
Amanda And Akko
People ship these two because of how friendly Amanda is toward Akko. This is very prominent in the episode, "Amanda and holy grail". Akko also thinks very highly of Amanda as her friend. Their ship name is Amandakko.
Akko And Andrew
People ship this purely for the fact that they seem to genuinely like each other and how Andrew thinks about Akko and magic in general. Lotte and Sucy often tease her about Andrew. In the episode "Bee Affection" he falls in love with Akko because of posion, but like with Diana, there may be truths behind it. Their ship name is Akkrew or Andakko.
Andrew And Frank
A lot of people ship this purely as a joke because they either don't ship Andrew with Akko, or they don't ship Lotte and Frank. Ship name is Andank or Franrew.
Frank And Lotte
In the episode "Bee Affection", Frank confesses his love for Lotte under the Cupid Bee's poison. Then after the poison stops it's effect, Frank still wants to go on a date with Lotte. Ultimately, she doesn't go on the date with Frank because she doesn't know him that well, but many people still ship it. Ship name is Frantte or Lotank.
Lotte And Sucy
Sucy and Lotte have been friends since the first episode and have helped each other life through numerous times Akko screws up. Whenever they aren't with Akko, they are seen hanging out in their room together. One of the reasons people ship it is because in the second to last episode Sucy comforts Lotte about Akko being lost. Ship name is Lotcy or Sutte.
Amanda, Akko, and Diana
Because both Diana and Amanda have shown favoritism towards Akko and therefore people ship it. There ship name is Amanakkana, Akkanana, or Diakkanda.
Jazmika, Constance, and Amanda
I don't really get why people ship this but yet there has been fics written about it. Ship name is Jazstanceanda, Conmikaanda, or Amikastance.
Chariot And Croix
Croix and Chariot have a checkered past together. They were both students at Luna Nova and helped each other with many things. Although they had there falling outs, by the end of the second season the two of them are friends again. What really makes people ship this is the fact that Chariot called out to Croix after she already left on her broom like a lover would in a romcom. Their ship name is Chariox.