If you're in the middle of the quest (meeting Rose with Timmy) there you can buy the first pair to progress. After that you can train with Rose several times to reach the next level, you could wear 3 inch max after that but right now the only heels you can buy are 2 inches, I'll add new ones in the future.
Point taken, I forgot to add the heels to the clothing shop that'll be there next version. Thongs weren't added originally, but I also added those so they will be available too.
Until then the only possible way to progress in the story should require the player to buy high heels during their quest when they visit a shop with Rose. They must buy at least one pair before they can move further so that's the only way of getting shoes at the moment.