Chloroantimonic vs fluoroantimonic acid
Chlroantimonic acid has been synthesised by dissolving antimony trioxide in concentrated hydrochloric acid followed by saturation with chlorine. The relevant information can be found here[1]:

Complex compounds are known to which the formulae $\ce{HSbCl6}$, $\ce{H2SbCl7 }$ and
$\ce{H3SbCl8}$ have been ascribed; these may be regarded as meta-, pyro- and
ortho-chlorantimonic acids [...] Neither the ortho- nor the
pyro-chlorantimonic acid appears to have been isolated, although salts
are known. Meta-chlorantimonic acid has been obtained by dissolving
antimony trioxide in concentrated hydrochloric acid and saturating the
solution with chlorine. The solution darkens at first, afterwards
changing to a bright greenish-yellow colour. Crystals can be obtained
by concentrating slightly over a water-bath, adding hydrochloric acid
and leaving over sulphuric acid, the temperature not
exceeing 0° C. The crystals are very hygroscopic; they are soluble in
cold water, alcohol, acetone and glacial acetic acid. The solution in
water undergoes hydrolysis, especially on warming, hydrated antimony
pentoxide separating out. It is prevented by
hydrochloric acid and to some extent by nitric acid. The solutions in
organic solvents are more stable. Various salts of chloroantimonic acid are known [...]

Bromoantimonic acid is prepared from crystallization from antimony bromide/bromine and sulfuric acid. From Here[2]:

Of the three possible acids only one has been obtained in the free
state. By crystallisation from a solution containing antimony
tri-bromide, bromine and either hydrobromic or sulphuric acid the
compound meta-bromoantimonic acid, $\ce{HSbBr6.3H2O}$, has been
prepared in the form of hygroscopic, irregular, six-sided, black
tablets. It decomposes readily, with evolution of bromine, leaving a
residue of antimony tribromide.

Pure iodoantimonic acid is not known although a mixed acid, $\ce{HSbBrI3}$ is known. Here[3]:

Salts of a complex antimony iodohydrobromic acid, $\ce{HSbBrI3}$, have
been obtained by triturating equimolecular proportions of antimony
triiodide and metallic bromide with a non-aqueous substance such as
acetic acid or xylene.

Carefully note that in this acid, antimony is in the +3 rather than +5 oxidation state.  Iodide ion, more easily oxidized than lighter halide ions, would accordingly be less stable in combination with antimony(V).
References

http://antimony.atomistry.com/chloroantimonic_acids.html

http://antimony.atomistry.com/antimony_pentabromide.html

http://antimony.atomistry.com/antimony_triiodide.html

$$\ce{Sb2O5 + 12HCl → 2H[SbCl6] + 5H2O}$$
http://www.easychem.org/en/subst-ref/?id=3722