Based on the list in Suffolk Dragonflies by Howard Mendel. (The accented syllables are in italics.)

aenea ay-nee-a
Aeshna eesh-na
AESHNIDAE eesh-nid-die
affinis aff-in-is
Anax an-ax
ANISOPTERA an-iss-op-terra
arctica ark-tik-a
armatum ar-mah-tum
barbarus bar-bar-us
boltonii boll-tony-eye
Brachytron brak-ee-tron
caerulea ki-roo-lee-a
CALOPTERYGIDAE cal-op-ter-ig-id-die
Calopteryx cal-op-ter-ricks
cancellatum can-sell-ah-tum
Ceriagrion kerri-ag-ree-on
Coenagrion coin-ag-ree-on
COENAGRIONIDAE coin-ag-ree-on-id-die
coerulescens coy-roo-less-kenns
Cordulegaster cor-dew-le-gas-ter
CORDULEGASTRIDAE cor-dew-le-gas-tri-die
Cordulia cor-dew-lee-a
CORDULIIDAE cor-dew-lee-i-die
Crocothemis cro-co-theme-iss
curtisii cur-tiss-ee-eye
cyanea sigh-a-nee-ah
cyathigerum sigh-a-thidge-er-um
danae dan– eye
depressa dee-press-ah
dryas dry-ass
dubia dew-bee-ah
elegans elly-gans
Enallagma enn-al-lag-mah
ephippiger ep-fip-ig-er
erythraea ery-thray-ah
Erythromma erry-thromm-ah
flaveolum flav-ee-oh-lum
flavescens flav-es-kens
fonscolombii fons-coll-omb-i-ee
fulva full-va
GOMPHIDAE gomm-fid-die
Gomphus gomm-fuss
grandis gran-diss
hastulatum hass-tew-lah-tum
Hemianax hem-ee-an-ax
imperator im-per-ah-tor
Ischnura ish-nure-ah
isosceles eye-soss-el-lees
juncea junn-kee-a
junius jun-ius
Lestes less-tees
LESTIDAE less-tid-die
Leucorrhinia lew-core-rin-nee-ah
Libellula lib-ell-yew-lah
LIBELLULIDAE lib-ell-yew-lid-die
lunulatum loon-yew-lah-tum
metallica met-al-i-ka
mixta mix-ta
mercuriale mer-cure-ee-ah-lee
meridionale mer-id-ee-on-ah-lee
najas nye-ass
nigrescens nig-gress-kenns
nymphula nim-few-la
ODONATA oh-doe-nah-ta
Orthetrum or-thee-trum (as in thesis)
Oxygastra oxy-gas-tra
Pantala pan-tah-lah
parthenope par-then-oh-pee
pedemontanum pee-dee-mont-ahnum
pennipes pen-nip-ays
PLATYCNEMIDIDAE plat-ick-nem-mid-id-die
Platycnemis plat-ick-nem-mis
pratense pra-tense-ay
puella poo-ell-a
pulchellum pull-kell-um
pumilio poo-mill-ee-oh
Pyrrhosoma pi-rho-so-ma
quadrimaculata quad-ree-mack-yew-lah-ta
sanguineum san-gwin-ee-um
scitulum scit-ewe-lum
Somatochlora so-matto-clor-ah
splendens splen-denns
sponsa spon-sah
striolatum stri-oh-lah-tum
Sympetrum sim-peat-rum
tenellum ten-ell-um
virgo ver-go
viridulum vir-id-youl-lum
vulgatissimus vul-ga-tiss-imus
vulgatum vul-gah-tum
ZYGOPTERA zy-gop-ter-ah