The kidnapper could be a power - hungry villain from another dimension. This villain has heard of Dr Flug's reputation and thinks that by kidnapping him, he can gain access to advanced technology. Or it could be a group of bounty hunters who were hired by someone who has a grudge against Dr Flug. They would capture him and deliver him to the person who hired them.
One possible plot could be that Dr Flug is kidnapped by a rival villain who wants to steal his inventions. Another plot might involve Dr Flug being kidnapped by an organization that wants him to work for them against his will. Or perhaps he's kidnapped by someone who has a vendetta against his boss and is using him as bait.
Maybe it's a cult leader. The cult might believe that Reid has some sort of special knowledge or power that they want to harness. They kidnap him to convert him to their beliefs or use his mind for their own strange purposes.
There are likely some out there. You could start by looking on fanfiction platforms like Archive of Our Own. Sometimes, these stories might explore the character of Dr Flug in difficult or 'hurt' scenarios within the context of the 'Villainous' universe. However, the availability and quality can vary.
It could be Dr. Eggman. He's always after Sonic and would love to get his hands on him to stop Sonic from foiling his evil plans. He might want to study Sonic's speed and use it for his own machines.
It could be Zeref. Since Zeref has an interest in powerful magic users and Natsu is a strong dragon slayer, Zeref might kidnap Natsu to study his magic or use him in some dark plan related to his quest for immortality or power.
It could be an orc warband. Orcs have always been enemies of the elves, and they might see Legolas as a valuable captive either for ransom or to torture. Another possibility is a rogue wizard. Wizards who have turned to the dark side often seek powerful beings to experiment on, and Legolas, with his elven magic and skills, would be an interesting subject.
As mentioned before, Eggman is a likely candidate. He's always had his eyes on Tails' skills and would stop at nothing to use them for his evil plans. So he could be the one behind the kidnapping.
It could be a jealous rival. Maybe someone who has always been in competition with Shawn in some aspect of his life, like work or a hobby, and decides to take drastic measures by kidnapping him.
It could be a group of rogue Decepticons who are acting on their own. They might not follow Megatron's orders but still see value in kidnapping Arcee. Maybe they have a personal vendetta against her or think they can get rich by selling her to the highest bidder in the Cybertronian underworld.
It could be an envious rival. Maybe someone who's always been in the shadow of Osomatsu and his brothers and decides to take matters into their own hands by kidnapping Osomatsu. Another option is a deranged collector. This person might see Osomatsu as a rare item to add to their collection of oddities. Or it could be a vengeful spirit. In a more supernatural setting, a spirit with a grudge against the Matsuno family could kidnap Osomatsu as a form of revenge.