Here are some markets that will either be closing or opening to submissions soon:
Abyss & Apex - open for poetry subs through June. (Will reopen to fiction subs in August.)
Acorn - will be open to subs during July and August.
Apex Magazine - will reopen to subs July 1st.
Flashquake - open to flash fiction subs through July 31st.
Frogpond - open to subs through August 1st.
Goblin Fruit - reopens to subs (fantasy poetry only) on July 9th.
Star*Line - open to subs for its prose poem issue now. Will reopen to general poetry subs July 1st.
Tales of the Talisman - closed for now, but will reopen to subs from July 1st through August 15th.
Vestal Review - reopens to subs (flash fiction) in August.
And here are some other paying markets to submit to:
Leading Edge - pays 1 cent/word for fiction ($10 minimum) and $10 per poem (if longer than 4 pages, $1.50 extra per page). Also provides two contributor copies.
Mayfly - pays $10/haiku.
OG's Speculative Fiction - pays $35/story and $10/poem.
The Pedestal Magazine - pays 8 cents/word for fiction and $40 per poem. From June 28th to August 14th, will only be considering flash fiction (1000 words or less).