Short version: no
Long version: no, they don’t.
There are several brands of the so-called ‘circulation boosters’ on the market that make cautious claims about boosting the circulation. The claims are made with caution as there is no evidence that they actually do. You often see them being promoted on the morning TV shows, in infomercials and commercials with celebrity endorsements (I have certainly lost respect for those that do endorse the circulation boosters). The concept behind a circulation booster is that it uses electric muscle stimulation to contract and relax the muscles, thereby increasing blood flow to your legs and feet. They may well do that for the short time that you are using that device, but the effect will last no longer. If you really want to boost your circulation then get out and go for a walk. That will do substantially more for improving your circulation than spending money on one of these devices.
The electrical stimulation may prove usual for some people with some type of neurological pain in their feet, so there is no shortages of testimonials that they “work” as they could help some of these problems. They do not help by improving the circulation. Despite the length of time that these have been on the market there is a distinct and obvious lack of scientific and medical research supporting their use.
Another way of looking at it, why are all the vascular surgeons not recommending the circulation boosters for their patients? There is a reason for that.
There is also a reason why so many are being sold second hand on eBay and Gumtree. That is because the circulation boosters no not really boost the circulation and so many are selling their devices.