Sounds like an aerial root, I believe the plant is an epiphyte, so its quite normal.

Can you post a picture? Aeschynanthus are epiphytic so it's likely a root. In humid climates they develop more readily. When you say "base of the flower" I think you're talking about where the inflorescence diverges from the vine. In that case it's very likely to be a root. All of my aeschynanthus have small nubs in a similar area that are the start of roots.

Mark

This prompted me to look at mine. It's not doing the same, but boy, does it need repotting! I just haven't even looked at it for the past year at least.

When you cut it back you can stick the cutting in the soil and they will grow so you will have a larger plant. Or you can root them in their own pot and share the wealth.
Carol