How to lose as little heat as possible to the surroundings from an endothermic reaction?
What is the scale?
What is the budget?


Reactors are available from 250 mL up.

It might be cheaper to place a flask in a cut-off bottom of a suitable PE bottle and insulate it with PU foam from a DIY market.

UPDATE

A small Dewar cylinder might be an option too. 
The model 00C has a volume of 100 mL and lids are available too. Usually, these Dewars are used to store liquid nitrogen and cooling mixtures (2-propanol + dry ice, etc.) so I don't know how resistant the lid is towards $\ce{HCl}$ over time. In addition, this setup isn't as tight as a flask with hollow stoppers and/or a silicone seal if that's an issue.