A colleague had such a device some years ago, but it depended on a touch interface that was a decade before there were touch interfaces. Theoretically it would not be hard to create such an interface, where a touch corresponds to F1/F2 values; then you simply synthesize the vowel with those formant values. Praat allows you to play around like that: see this question with comments on how to create a synthesis script (it would be easier in the case of just a vowel rather than a CV transition). There is an online Klatt synthesis interface here, where you can specify all of the formants and anything else of interest. The hard part is mapping from intuitive vowel positions to actual formant values (which is not terribly hard).
For educational and entertainment purposes, I highly recommend using the online Klatt program and play with formant values, not being bound by empirically-justified limits on particular formants: see what happens when F1 is 1800, and thereby find the boundaries between vowel-like sounds and machine-buzzing noises. This gave me an appreciation for the importance of F1.
As noted by Jeremy Needle, Pink Trombone kind of approaches the desideratum of an articulation-based synthesizer (it looks "backwards", i.e. the vocal tract looks rightwards). With a mouse you can only change one articulatory setting at a time, but with a touch screen, you can get multiple constrictions. You could use Audacity sound capture to extract samples and find formants.