The Web Speech API built into browsers doesn't do IPA, so I had to use Ivona.
So I had to build myself a tiny little Spark backend.
mvn clean package
cf push
To run locally:
java -cp target/tts-0.0.1-jar-with-dependencies.jar PhonemesToSpeech
Then you can GET http://localhost:4567/pts?word={someIPA}.
For it to work, you'll need to sign up for Ivona and put your credentials into src/main/resources/IvonaCredentials.properties in this form:
accessKey = {your access key}
secretKey = {your secret key}