No, there is no scientific basis for this claim. Dr Andrew Weil has this to say:
Massage certainly can help address the build up of lactic acid in muscles, and promote the clearing of normal byproducts of muscle metabolism, but I know of no evidence suggesting that massage can remove toxins of any kind from the body.
This Massage Today article written by Keith Eric Grant, PhD, NCTMB, elaborates:
There's a statement, seemingly pervasive throughout massage education
and massage books, that unspecified toxins accumulate in the body, and
that these toxins can be flushed out by massage. I believe this is yet
another myth that continues to be passed on as misinformation to
massage students. This is not to dispute that there are very real
toxins that accumulate in the body, notably persistent organic
pollutants (POPs) in fatty tissues and heavy metals in skeletal
tissues. However, these toxins are too chemically bound to their
target tissues to be significantly liberated by the mechanical motions
There's an NIH study showing that massage is not effective for removal of lactic acid buildup:
This investigation highlights the comparison of blood lactate removal
during the period of recovery in which the subjects were required to
sit down as a passive rest period, followed by active recovery at 30%
VO(2)max, and short term body massage, as the three modes of recovery
used.... Analysis of lactate values indicated no remarkable difference
between massage and a passive type of sitting recovery period. It was
observed that in short term massage recovery, more oxygen was consumed
as compared to a passive type of sitting recovery. It is concluded
from the study that the short term body massage is ineffective in
enhancing the lactate removal and that an active type of recovery is
the best modality for enhancing lactate removal after exercise.
The primary issue with this claim is that it uses the "alternative medicine" definition of toxin:
In the context of alternative medicine the term is often used to refer to any substance claimed to cause ill health, ranging anywhere from trace amounts of pesticides to common food items like refined sugar or additives such as monosodium glutamate (MSG).
You will never get a clear definition of what "toxins" are in this sense, and so "flushing toxins" should be bundled in with fad "detox diets" whose claimed benefits are not supported by evidence.
Additionally, actual toxins are naturally "flushed" from the body:
Most ingested toxins are efficiently and effectively removed by the kidneys and liver and excreted in urine and stool.
Skepdic also mirrors my sentiments:
Some claim juice fasting is the key to detoxification. Others claim a raw food or vegetarian diet is the best detox therapy. Some swear by enemas; others by ozone therapy, acupuncture, and massage. Others swear by mega-vitamins and antioxidants. Some swear you shouldn't eat anything but fruit until noon so the body can detox properly. Again, none of the proponents of these methods name a single toxin that is removed, in what quantity, or with what specific benefit.
And Sense about Science (PDF) has something similar to say - and that, as with everything, the dose makes the poison:
Claim 1: Toxins have built up in the body and
need to be flushed/cleansed from it
The terms ‘toxic’ or ‘toxins’ are used to imply that a
chemical is causing you harm. In reality all chemicals
can be toxic and it is the dose that is important e.g.
one 400 g Vitamin A tablet may be beneficial but
taking 20 of these at once could damage your liver.
Most chemicals do not accumulate in the body – they
are removed by the liver and kidney. Many of the
detox products which claim to flush the body of
chemicals contain diuretics, which increase the
amount you urinate. This just removes water and