Can vaccines harm helminths?
The BCG vaccine was identified in a 2023 study as a possible new approach to the treatment of helminth infections.
- The double-sided effects of Mycobacterium Bovis bacillus Calmette-Guérin vaccine on helminthic infections
However, there have been no reports of adverse effects on therapeutic helminths following receipt of the BCG vaccine.
The only other suggestions that vaccines might harm therapeuutic helminths were made in posts to the helminthic therapy support groups and concerned the tetanus and influenza vaccines. Three members of the now-discontinued Yahoo Helminthic Therapy forum claimed that they may have lost their hookworms following tetanus immunisation, although this is by no means certain.
Someone posted the following comment to the Facebook Helminthic Therapy Support group after a flu vaccination.
It is possible that the return of disease symptoms following a vaccination could be due to the immune response to the immunisation temporarily overwhelming the activity of the worms, as is explained here. And, although the subject in the latter case is convinced that she only regained benefits once she had reinoculated, it is coneivable that, having been temporatily ovewhelmed by the immune response to the vaccine, her helminths may have resumed providing benefits to coincide with reinoculation.
Another hookworm host has reported that the flu vaccine - which she gets every year - doesn’t affect her worms other than perhaps to dampen their effects for a short while. 
Several other self-treaters have received vaccines, including flu shots, without any adverse effect on their worms.
Considering that people have been deliberately infecting themselves with helminths since 2003, and that there were an estimated 6,000-7,000 helminth self-treaters in 2015,  it is likely that there would have been more reports about this if vaccination were a common issue.
The anti-hookworm vaccine
One vaccine that will undoubtedly harm hookworms is the anti-hookworm vaccine that is currently in clinical development.  Unfortunately, not only will an effective hookworm vaccine rid those who take it of their hookworms, it may possibly cause allergic reactions  and may also deny its users the opportunity to use controlled therapeutic doses of this species to treat the autoimmune, inflammatory and allergic diseases that will be more likely to appear as a result of the loss from their biomes of this keystone species. 
This risk appears not to be on the radar of those involved in the vaccine’s development, but the work of other academics has shown that effective control of exposure to hookworms could be provided by alternative measures such as the provision of information and education, improvements to basic sanitation and access to safe, clean water, possibly supplemented by periodic deworming, although deworming is also of questionable benefit.
- Effect of sanitation on soil-transmitted helminth infection: systematic review and meta-analysis -- Full text | PDF
Can helminths adversely affect vaccine efficacy?
Helminths may interfere with some vaccine responses,  and it has been suggested that they might have a detrimental effect on vaccine efficacy,  with one study reporting that a helminth infection suppressed the efficacy of a seasonal influenza vaccine in a mouse model. 
However, other evidence suggests that helminth colonisation in humans is unlikely to adversely affect vaccine efficacy.
Parasite exposure has been found not to be associated with a reduced response to pneumococcal conjugate vaccine or a malaria transmission blocking vaccine.
- Chronic helminth infection does not impair immune response to malaria transmission blocking vaccine Pfs230D1-EPA/Alhydrogel® in mice
The presence of helminths may actually enhance the beneficial effect of vaccines, as was indicated in one study in which enhanced biodiversity (of worms and bacteria) was shown to be associated with better immune responsiveness, including better responses to vaccination, better T-cell responses, and much higher levels of "natural" antibodies shown to be important in fighting cancer. 
Can helminths help reduce vaccine side effects?
Helminths may help reduce the side effects caused by a dose of vaccine by modulating the immune system's response to it. 
Can helminths help to treat vaccine injuries?
If an autoimmune condition has been triggered by vaccination (for example, SLE or RA , or ASIA/Shoenfeld’s Syndrome ) this may be amenable to helminthic therapy in the same way that other autoimmune diseases are.
Another disease that can be triggered by vaccination is Guillain–Barré syndrome, in which the body's immune system mistakenly attacks the peripheral nerves and damages their myelin insulation following invasion by a foreign antigen.  Since helminths are able to counter a misdirected immune response, it is conceivable that helminthic therapy might help in treating this condition.
Until quite recently, medical treatments for Guillain–Barré syndrome and other autoimmune diseases have tended to concentrate on attacking the “bad” effector cells, but a treatment reported in early 2012, and shown to be successful against Guillain–Barré syndrome in rats, increased the "good" regulatory cells. Not only did the sick rats recover much more quickly as a result of this treatment, but those treated prophylactically did not fall ill.  The authors of this study point to the fact that their treatment has a similar effect to that observed in patients infected with helminths, both of which approaches regulate the immune system and boost T-cell production in a similar manner.
The effect of vaccines on helminthic therapy
Vaccines are designed to induce active acquired immunity to an infectious agent by challenging the recipient’s immune system with a weakened or killed form of a microorganism, or with one of its products, or a synthetic substitute. The immune system responds to this “infection” in the same way that it would to a live infection, and the resulting increase in immune activity can temporarily overwhelm the more subtle effects of helminths, effectively reducing the benefits they produce.
For more about this, see How infections impact on the benefits of helminthic therapy.