Can states buy vaccines directly from the manufacturers?
Yes, for childhood vaccines, under the Vaccines For Children (VFC) program, where children may not qualify as "federally vaccine-eligible children". In those cases, the state may purchase vaccines from the manufacturers.
42 U.S. Code § 1396s - Program for distribution of pediatric vaccines
(d)(4)(B) each State, at the option of the State, shall be permitted to obtain additional quantities of pediatric vaccines (subject to amounts specified to the Secretary by the State in advance of negotiations) through purchasing the vaccines from the manufacturers at the applicable price negotiated by the Secretary consistent with paragraph (3), if (i) the State agrees that the vaccines will be used to provide immunizations only for children who are not federally vaccine-eligible children ...
Whether this will apply to COVID-19 vaccines, under VFC, has not been decided, yet.
The CDC will determine if COVID-19 vaccine(s) will be included in the VFC program. If they are included, then Medicaid will cover the administration fee for Medicaid-eligible children. — Kaiser Family Foundation
[A]re there any federal guidelines that prohibit states from procuring vaccines directly from the manufacturers?
Relevant to the vaccine for COVID-19, in the Bloomberg article, linked from the question and referring to Phizer —
The company said it’s open to collaborating with the U.S. Department of Health and Human Services in a way "that will allow the drugmaker to quickly distribute its vaccine to as many Americans as possible."
"However, before we can even consider direct sales to state governments, HHS would need to approve that proposal based on the EUA granted to Pfizer by the FDA," the New York-based company said in a statement.
EUA is Emergency Use Authorization
The EUA for Pfizer does allow the distribution, but not the sale, to a state. And distribution is controlled by the US under Operation Warp Speed.
In a letter to Phizer, from the FDA, dated December 23, 2020,
On December 11, 2020, the Food and Drug Administration (FDA) issued an Emergency Use Authorization (EUA) for emergency use of Pfizer-BioNTech COVID-19 Vaccine for the prevention of Coronavirus Disease 2019 (COVID-19) for individuals 16 years of age and older, as described in the Scope of Authorization (Section II) of this letter; ...
Later, in the Scope of Authorization,
I have concluded, pursuant to Section 564(d)(1) of the Act, that the scope of this authorization is limited as follows:
Pfizer Inc. will supply Pfizer-BioNTech COVID-19 Vaccine either directly or through authorized distributor(s), to emergency response stakeholders as directed by the U.S. government, including the Centers for Disease Control and Prevention (CDC) and/or other designee, for use consistent with the terms and conditions of this EUA;
...
Where, in a footnote, "emergency response stakeholder" includes states.
Update
White House says U.S. states can’t directly purchase Covid vaccine under emergency use authorization, January 24, 2021.
Key points
White House chief of staff Ron Klain said Sunday that it’s not possible for states to purchase Covid-19 vaccines directly from manufacturers.
The comments come after New York Gov. Andrew Cuomo asked Pfizer on Monday to purchase vaccines directly from the company, citing tightening supply.
“As a matter of law, this vaccine is under an emergency use authorization,” Klain told NBC when asked about the requests. “I don’t think that’s possible,” Klain said.
