There is no direct connection between Sri Chinnamasta (vajra-vairochani) and Lord Sri Indra. But Vajra has meaning apart from the powerful weapon.
Vajra is a Sanskrit word meaning both thunderbolt and diamond. Additionally, it is a weapon won in battle which is used as a ritual object to symbolize both the properties of a diamond (indestructibility) and a thunderbolt (irresistible force).
The vajra is the weapon of the Vedic rain and thunder-deity Indra, and is used symbolically by the dharma traditions of Buddhism, Jainism and Hinduism, often to represent firmness of spirit and spiritual power. The use of the vajra as a symbolic and ritual tool spread from India along with Indian religion and culture to other parts of Asia.
In Buddhism the vajra is the symbol of Vajrayana, one of the three major branches of Buddhism. Vajrayana is translated as "Thunderbolt Way" or "Diamond Way" and can imply the thunderbolt experience of Buddhist enlightenment or bodhi. It also implies indestructibility, just as diamonds are harder than other gemstones.
Thus chinnamastA does not essentially carry a vajra like indra but yes she is associated with thunderbolt, lightning, brilliance, electric energy (vidyuta shakti) etc. Chinnamasta is the thunder goddess. With a flash of lightning and thunder she destroys ignorance, severs identity with the physical body.She is about direct perception and regaining freedom.
The name vajra vairochani and prachanDa/mahA ChanDa chaNDikA are related to her fierce and lightening personality. The reference of these names can be found in Sri Chinnamasta ashtottara shata nAma of Shakta pramoda which are given below.
mahAchaNDA chaNDa-rUpA chaNDikA chaNDa-khaNDinI /
krodhinI krodha-jananI krodha-rUpA kuhU kalA // 5 //
Most terrifying, of terrible form, the terrifying one, the slaughterer of chaNDa; the wrathful one, the generator of wrath, of form of wrath, of form of the new-moon phase
kopAturA kopayutA kopa-saMhAra-kAriNI /
vajra-vairochanI vajrA vajra-kalpA cha DAkinI // 6 //
inciter of fury, conjoined with fury, the destroyer of fury;
vajra-vairochanI, of the form of the thunderbolt, a manifestation of the thunderbolt and a DAkini (a companion of the goddess)